College Algebra
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The formula for the difference quotient is [f(x + h) - f(x)]/h, h ≠ 0. Use this formula to calculate the difference quotient of the following function:
f(x) = 3x2 + 7x - 9
A line passes through (- 4, - 11) and is perpendicular to x - 6y + 24 = 0. Represent the equation of this line in point-slope form and slope-intercept form.
Find the slope, m, and y-intercept, b, of a linear function, f(x) = mx + b given the following:
f(2) = 8, f(6) = -4
List the possible rational zeros of the following equation using Rational Zero Theorem. Then, use synthetic division to find an actual zero. Find the remaining zeros using the quotient from division: 9x3 + 27x2 - 40x - 16 = 0
For the given conditions: x-intercept = 1/5, y-intercept = 10
Write an equation for the line in Slope-intercept form by first going through the point-slope form.
For the given conditions: Passing through (- 2, 0) and (4, - 9)
For the given conditions: Passing through (- 6, - 2) and (- 4, 4)
The graph of a linear function is perpendicular to the line whose equation is 5x -f(x) = -5 and passes through (-2, 0). State the equation of this function in slope-intercept form.
Consider the given equation and determine the rate of change from x1 to x2.
f(x) = x1/3 +x from x1 = 8 to x2 = 27
Write the equation of the line in slope-intercept and point-slope form using the given conditions. Point on the line (4, -1), perpendicular to the line x +3y -7 = 0
Write the equation of the line in slope-intercept form using the given conditions. Point on the line (-1, -3), parallel to the line 3x -y +4 =0
Use the slope-intercept form and point-slope form to write the equation of the line shown.
For the given slope 4 and a point on the line given as (1, 2), determine the y-intercept of the line.
For the given linear function, draw the graph in the rectangular coordinate system. 2f(x) = 4x +1
A pair of two points for the line and the slope is given below. Find the value of x satisfying the given data. (x, 3), (2x, 1); m = -2
For the given equation, determine the slope and y-intercept. Px +Qy +R = 0
Evaluate the slope of the line using the two points given and state the nature of the slope. Assume all variables represent positive real numbers. (-a, a), (b, -b)
By using intercepts, draw the graph of the given equation in the rectangular coordinate system. 2x +y = 8
For the given conditions: Passing through (- 17, 0) and (0, 17)
Consider the given equation and draw the graph of the equation in the rectangular coordinate system. y = √2
Graph the linear function after determining the slope and y-intercept. y = 3x/4 +2
Graph the linear function after determining the slope and y-intercept. y = 5x +7
For the given conditions: Slope = - 1/8, passing through (4, - 8)
For the given conditions: Slope = - 2, passing through (- 3, - 1/3)
For the given conditions: Slope = - 7, passing through (- 3, - 19)
For the given conditions: Slope = 10, passing through (2, - 5)
For the given conditions: Slope = 4, passing through (1, 9)
Find the slope of the line passing through the following points:
(- 7, - 2) and (1, - 18)
Indicate if the line rises or falls or if it is horizontal or vertical.
(- 4, 7) and (- 1, 10)
(13, 11) and (1, 5)
Solve for b to express b as a function of a.
11a - 3b + 7 = 0
Find the x- and y-intercepts (___, 0) and (0, ___) that will satisfy the equation 9x - 3y + 27 = 0.
Find the slope (y2 - y1)/(x2 - x1) if (x1, y1) = (- 1, 5) and (x2, y2) = (- 5, 9).
A line that passes through (7,-2) is perpendicular to the line defined by y = (3/5)x + 8. Determine the equation of this line both in slope-intercept and point-slope form.
A line that passes through (5,-6) is parallel to the line 2x + y + 4 = 0. Determine the equation of this line both in slope-intercept and point-slope form.
A line with a slope of -2 passes through the point (4, 5). Determine the equation of the line both in slope-intercept and point-slope form.
Calculate the slope of the line that passes through the points (-6, -3) and (2, -5) or identify if the slope is undefined. Also, identify the orientation of the line (horizontal, vertical, rises, falls).
Which of the following expressions shows the difference quotient [f(x + h) - f(x)]/h, h =/= 0 of f(x) = 3x2+5x-2?
Find the equation of a line passing through the point (5, 8) and having a slope(m) equal to -6. Write the equation in the standard form.
Find the equation of a line passing through the point (-7, 3) and having a slope (m) equal to -5/3. Write the equation in the standard form.
Find the equation of a line passing through the point (-10, 9) and has undefined slope (m). Write the equation in the standard form.
Find the equation of a line passing through the points (-3, 5) and (7, 6) Write the equation in the standard form.
Find the equation of a line having x-intercept and y-intercept equal to (5, 0) and (0, -4) respectively. Write the equation in the slope-intercept form.
Find the equation of a horizontal line passing through a point (-9, 8). Write the equation in the slope-intercept form.
Find the equation of a line with m = 8 and b = 13. Write the equation in the slope-intercept form.
Sketch the graph using the given equation:y = 96
Find the equation of a line with slope and y-intercept equal to 0 and (0, 5/3) respectively. Write the equation in the slope-intercept form.
Determine the y-intercept and the slope of the line defined by the following equation. Then, graph the line.
15x - 60y = -42
Determine the y-intercept and the slope of the line defined by -4x + 2y -1 =0. Then, graph the line.
Determine the x-intercept, y-intercept, and the slope of the line whose graph is shown. Also, write a linear function f that represents the line.
Graph the line 8x - 3y +2 = 0 by using both of its x and y-intercepts.
A hypothetical line passes through the points (0, - 13) and (29, - 13). What is its slope?
Consider a line defined by 2x + y = 7. Write equations (both in standard and slope-intercept form) of a line that is parallel to the given line and passes through (-4,2).
Determine the slope for the given line and plot it on the rectangular coordinate system. 8x -3y = 27
Consider a line defined by x = 7. Write equations (both in standard and slope-intercept form) of a line that is perpendicular to the given line and passes through (12,-8).
Graph the given linear function using slope and intercept after showing the given equation in slope-intercept form. Also, write the slope and y-intercept. (1/2)x +7y +1 = 0
Find the equation that describes a line which passes through (- 1, 8) and (5, 7). Express in both slope-intercept form and standard form (if possible).
Find the equation that describes a line which passes through (9, - 13) and is perpendicular to a line with an undefined slope. Express in both slope-intercept form and standard form (if possible).
Find the equation that describes a line which passes through (0, 11) and is perpendicular to the line 9x + 2y = 5. Express in both slope-intercept form and standard form (if possible).
Consider the given graph.
What is the average rate of change illustrated? And what does it mean?
Solve the following equation by using a graphing utility:
4(3x - 5) - 6(x - 7) = 7