This document provides examples of writing equations of linear functions in different forms: - Slope is defined as the rise over the run and is used to find equations in point-slope form. - Vertical lines have undefined slope while horizontal lines have a zero slope. - Examples show writing equations in point-slope, slope-intercept, and standard form by given a slope and point or through manipulation of variables. - Standard form is defined as Ax + By = C.

1. Module 4 Topic 3 More – Writing Equations of Linear Functions

2. Example 1 Slope = m The formula to find slope is; (y2 - y1) ÷ (x2 - x1)

3. Example 2 What is the slope of a vertical line? Vertical lines have no slope so they are undefined.

4. Example 3 What is the slope of a horizontal line? Horizontal lines have a slope of zero!

5. Example 4 Similar Problem: Find the slope of the line that passes through (-3, 6) and (-4, 4). m = (4 - 6) ÷ (-4 - -3) m = -2 ÷ -1 m = 2

6. Example 5 Point-Slope form is y2 - y1 = m(x2 - x1)

7. Example 6 Similar Problem: Write the equation of the line in point-slope form that has a slope of -4/5 and passes through the point (3, 11). y2 - y1 = m(x2 - x1) y - 11 = -4/5 (x - 3)

8. Example 7 Similar Problem: Write the equation of the line in slope-intercept form that has a slope of -4 and passes through the point (2, 0). y = mx + b 0 = -4(2) + b 0 = -8 + b 8 = b y = -4x + 8

9. Example 8 What is the equation for Standard Form? Ax + By = C

10. Example 9 Similar Problem: Change the linear equation y - 8 = 4(x - 3) to Standard Form. y- 8 = 4(x - 3) Solve for y. Distribute 4. y- 8 = 4x – 12 Add 8 to each side. y= 4x - 4