Writing Linear Functions

1. Module 4 Topic 3 Writing Equations of Linear Functions

2. Example 1 Similar Problem: What is the equation in slope-intercept form of the following? Let's pretend that the x-intercept is 3 so the ordered pair would be (3, 0) and the other ordered pair is (1, 1). 1) Find the slope. (3, 0) and (1, 1) m = (1 - 0)/(1 - 3) = 1/-2 m = -1/2 2) Use the slope and either point to plug into point-slope form, let's use (1, 1) y - y = m(x - x) y - 1 = -1/2(x - 1) y - 1 = -1/2 x + 1/2 y = -1/2 x + 3/2

3. Example 2 Similar Problem: What is the equation of the following line? Anytime there is a horizontal line the equation of the line is always going to be y = y. If you were to take the ordered pairs off of the line given you would have (2, 3), (5, 3), (4, 3), (-2, 3), etc. So the equation of the line is y = 3.

4. Example 3 Similar Problem: What is the equation of the following line? Anytime there is a vertical line the equation of the line is always going to be x = x. If you were to take the ordered pairs off of the line given you would have (2, 0), (2, 1), (2, 2), (2, 3), etc. So the equation of the line is x = 2.

5. Example 4 Similar Problem: Write an equation in slope-intercept form of the line that passes through the point (-5, 2) and has a slope of -5/4. Use the point and the slope and plug into point-slope form. Solve for y. y - y = m(x - x) y - 2 =-5/4 (x - -5) y - 2 = -5/4 (x + 5) y - 2 = -5/4 x + -25/4 y = -5/4 x - 17/4

6. Example 5 Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)? 1) Find the slope. m = (9 - -1)/(-2 - 3) m = 10/-5 = -2 2) Use the slope and either point to plug into point slope form, let's use (3, -1) y - y = m(x - x) y - -1 = -2(x - 3) y + 1 = -2(x - 3) y + 1 = -2x + 6 y = -2x - 5

7. Example 6 Similar Problem: Write the equation in slope-intercept form: 6x - 4y = 24. 6x - 4y = 24 (solve for y.) Subtract 6x to both sides. -4y = -6x + 24 Divide each side by -4. y = 3/2 x - 6

8. Example 7 Similar Problem: Write the equation in slope-intercept form: 6x - 4y = 24. 6x - 4y = 24 (solve for y.) Subtract 6x to both sides. -4y = -6x + 24 Divide each side by -4. y = 3/2 x - 6

9. Example 8 Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)? 1) Find the slope. m = (9 - -1)/(-2 - 3) m = 10/-5 = -2 2) Use the slope and either point to plug into point slope form, let's use (3, -1) y - y = m(x - x) y - -1 = -2(x - 3) y + 1 = -2(x - 3) y + 1 = -2x + 6 y = -2x - 5

10. Example 9 Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)? 1) Find the slope. m = (9 - -1)/(-2 - 3) m = 10/-5 = -2 2) Use the slope and either point to plug into point slope form, let's use (3, -1) y - y = m(x - x) y - -1 = -2(x - 3) y + 1 = -2(x - 3) y + 1 = -2x + 6 y = -2x - 5