1. 2.6 Finding equations of lines

2. Review Slope-Intercept Form: y = mx + b Point-Slope Form: y – y 1 = m (x – x 1 )

3. Ex 1) Find the linear equation if you know slope m = -3 and y-intercept is (0,5) We have y = m x + b So y = -3x + 5

4. Practice Find the linear equation if you know slope m = - ½ and y-intercept is (0,1)

5. Ex2) Find a linear equation that has slope = 2 and passes through (3,5) m = 2, and (3,5) Using Slope-Intercept form Y = mx + b 5 = 2(3) + b 5 = 6 + b -1 = b So y = 2x - 1 m = 2, and (3,5) Using Point-Slope Form y – y 1 = m (x – x 1 ) y – 5 = 2 (x – 3) y – 5 = 2x - 6 y = 2x – 6 + 5 y = 2x - 1 x y x 1 y 1

6. Practice Find a linear equation that has slope = -5 and passes through (-4,2)

7. Ex3) Find a linear equation that passes through (-2,-3) and (-4,-6) Find the slope m: y 1 – y 2 -3- (-6) 3 x 1 – x 2 -2 + 4 2 Use Slope-Intercept Form y= mx + b -3 = (3/2)(-2) + b -3 = -3 + b 0 = b y = (3/2) x = =

8. Practice Find a linear equation that passes through (-3,-5) and (-4,12)

9. Ex4) Find a linear equation that // to y = 2x + 1 and passes through (3,9) m = 2, and (3,9) Y = mx + b 9 = 2(3) + b 9 = 6 + b b = 3 Y = 2x + 3

10. Practice Find a linear equation that // to 9x – 3y =5 and passes through (2,-1)

11. Ex5) Find a linear equation that to y = (1/3)x - 11 and passes through (-1,4) m = -3, and (-1,4) Y = mx + b 4 = -3(-1) + b 4 = 3 + b b = 1 Y = -3x + 1

12. Find a linear equation that to 2x – 4y = 9 and passes through (5,4)

13. F(t) = -25t + 750 30