2. Graphs of Equations

Practice this topic

Find the slope of the line shown below.

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Find the slope of the line containing the points $\left(-1,1\right)$ and  $\left(4,3\right)$ .

Write an equation of a line that passes through the point $\left(3,-4\right)$ and is parallel to the line  $x+2y+18=0$ .

Graph a line with a slope of 0 that passes through the point $\left(3,-2\right)$ .

Which of the following graphs below represents the equation $x=3$ ?

In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

Identify the 𝒚– intercept & slope of  $y=-2x-3$ . Then graph the equation.

234

Write the point-slope form of the equation of a line with a slope of $-\frac25$ that passes through (1, 3). Then graph the equation.

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Write the point-slope form of the equation of a line with a slope of $0$ that passes through $\left(2,-4\right)$ . Then graph the equation.

467

Write the point-slope form of the equation of a line that passes through the points $\left(2,1\right)$ and  $\left(-4,3\right)$ . Then graph the equation.

702

Find the slope & $y-intercept$ of the line given by the equation $3x+2y-6=0$

482

Graph the equation $9x+6y+18=0$ by finding the intercepts.

449

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.

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In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-2, 1) and (2, 2)

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In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general form. Passing through (−2, 2) and parallel to the line whose equation is 2x-3y-7=0

472

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (1,3), m = -2

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Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-5,4), m = -3/2

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In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 8, passing through (4, −1)

In Exercises 13-18, find the average rate of change of the function from 1 to 2. f(x) = x² + 2x from x₁ = 3 to x2 = 5

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Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-8,4), undefined slope

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Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

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In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−2, 6) and is perpendicular to the line whose equation is x = -4.

468

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

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In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. x^4−2x^3−5x^2+8x+4=0

230

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)

204

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. m=5, b=15

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In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2, 0) and (0, 2)

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Match each equation with the sketch that most closely resembles its graph. y = 5

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Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)

339

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

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In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 2) with slope - 6

589

Find the slope and y-intercept of each line, and graph it. x+2y = -4

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In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0

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In Exercises 49–58, graph each equation in a rectangular coordinate system. y = -2

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The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

965

Graph using intercepts: 2x - 5y - 10 = 0

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Find the slope of each line, provided that it has a slope. through (0, -7) and (3, -7)

222

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5

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For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 5x - 2y = 10

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Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, -4), perpendicular to x=4

240

In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 4x+y-6=0

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For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (-2, 4) and (1, 3)

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For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (2, -10), perpendicular to a line with undefined slope.

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For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (0, 5), perpendicular to 8x+5y=3

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Find and interpret the average rate of change illustrated in each graph.

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Use a graphing calculator to solve each linear equation. 3(2x+1) - 2 (x-2) =5

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In Exercises 67–72, use intercepts to graph each equation. 6x-3y+15=0

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In Exercises 79–80, find the value of y if the line through the two given points is to have the indicated slope. (3, y) and (1, 4), m = −3

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Retaining the Concepts. If f(x) = 4x^2 - 5x - 2, find [f(x + h) - f(x)]/h, h ≠ 0

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Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and (x2, y2) = (−2, 4), find (y2-y1)/(x2-x1)

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In Exercises 67–72, use intercepts to graph each equation. 6x-9y-18 = 0

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Graph each line. Give the domain and range. x = -4

Graph each line. Give the domain and range. -3x + 6 = 0

Graph each line. Give the domain and range. -x + 5 = 0

Graph each line. Give the domain and range. 3 + x = 0

Match each equation with the sketch that most closely resembles its graph. x = 5

If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.)

Find the slope of the line satisfying the given conditions. See Example 5. through (2, -1) and (-3, -3)

Find the slope of the line satisfying the given conditions. See Example 5. through (-3, 4) and (2, -8)

Find the slope of the line satisfying the given conditions. See Example 5. through (5, 9) and (-2, 9)

Find the slope of the line satisfying the given conditions. See Example 5. horizontal, through (5, 1)

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (-7, 4), perpendicular to y=8

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (3, -5), parallel to y=4

Find the slope of each line, provided that it has a slope. through (2, -2) and (3, -4)

Find the slope of each line, provided that it has a slope. through (8, 7) and (1/2, -2)

Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

Find the slope of each line, provided that it has a slope. 11x + 2y = 3

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (3, -5) with slope -2.

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. x - intercept (-3, 0), y-intercept (0, 5)

Find the slope of the line satisfying the given conditions. See Example 5. vertical, through (4, -7)

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. y = 2x - 4

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 2y = -3x

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 4x + 3y = 12

Graph the line satisfying the given conditions. through (2, -4), m = 3/4

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (-2, 8), m = 2/5

Graph the line satisfying the given conditions. through (0, 5), m= -2/3

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (3, -4), m = - 1/3

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through ( - 1/2 , 4), m = 0

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (9/4 , 2), undefined slope

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (- 5/2 , 3), undefined slope

Find and interpret the average rate of change illustrated in each graph.

In Exercises 49–58, graph each equation in a rectangular coordinate system. 3x -18=0

Write an equation in point-slope form and slope-intercept form of the line passing through (-10,3) and (-2,-5).

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. y = (2/5)x - 1

Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope ______ and y-intercept ______.

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-2, -2), parallel to y=3

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, 1), parallel to y=-5

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15

Use a graphing calculator to solve each linear equation. 7x-2x+ 4-5=3x+1

If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1, -3), (-5, 12), (1, -11)

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (5,-8), m = 0

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. vertical, through (-6, 4)

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-2,5) having slope -4

Find the slope and y-intercept of each line, and graph it. 4x-y =7

106

Find the slope and y-intercept of each line, and graph it. 4y = -3x

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.