1. 2.4 – Writing Linear Equations

2. 2.4 – Writing Linear Equations Forms:

3. 2.4 – Writing Linear Equations Forms: Standard Form

4. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C

5. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form

6. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b

7. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form

8. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 )

9. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point

10. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1).

11. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given:

12. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2

13. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1)

14. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope

15. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 )

16. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4))

17. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4)

18. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6

19. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6

20. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6 + 1 + 1

21. 2.4 – Writing Linear Equations Forms: Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) Example 1 - Write an Equation Given Slope & a Point Write and equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1). Given: m = -3/2 (-4,1) Point-Slope y – y 1 = m(x – x 1 ) y – 1 = (-3/2)(x – (-4)) y – 1 = (-3/2)(x + 4) y – 1 = (-3/2)x – 6 + 1 + 1 y = (-3/2)x – 5

22. Example 2 Write an Equation of a Perpendicular Line

23. Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1.

24. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3)

25. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4

26. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼

27. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼.

28. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 )

29. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4))

30. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4)

31. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4) y – 3 = ¼(x) + ¼(4)

32. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4) y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1

33. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4) y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1 + 3+ 3

34. Example 2 Write an Equation of a Perpendicular Line Write an equation for the line that passes through (-4,3) and is perpendicular to the line whose equation is y = -4x – 1. (-4,3) m 1 = -4 m 2 = ¼ So, write eq. through (-4,3) w/m 2 = ¼. y – y 1 = m(x – x 1 ) y – 3 = ¼(x – (-4)) y – 3 = ¼(x + 4) y – 3 = ¼(x) + ¼(4) y – 3 = ¼(x) + 1 + 3+ 3 y = ¼(x) + 4