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

Verified step by step guidance

1. Identify the given information: a point (5, -8) and a slope m = 0.
2. Recall that a slope of 0 indicates a horizontal line.
3. The equation of a horizontal line passing through a point (x_1, y_1) is y = y_1.
4. Substitute the y-coordinate of the given point into the equation: y = -8.
5. Convert the equation y = -8 into standard form, which is Ax + By = C. For a horizontal line, this becomes 0x + 1y = -8.

Key Concepts

Point-Slope Form of a Line

The point-slope form of a line is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful when you know a point on the line and the slope, allowing you to easily write the equation of the line.

Slope-Intercept Form

The slope-intercept form of a line is given by the equation y = mx + b, where m represents the slope and b is the y-intercept. This form is advantageous for quickly identifying the slope and where the line crosses the y-axis, making it easier to graph the line.

Standard Form of a Line

The standard form of a line is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for solving systems of equations and can be converted to slope-intercept form for graphing purposes.