1. Writing Linear Equations from Ordered Pairs
Algebra 1

2. Learning Targets
Write an equation in slope-intercept form from a slope and point
Write an equation in slope-intercept form from two points
Write an equation in point-slope form from a slope and point
Write an equation in point-slope form from two points

3. Writing Linear Equations: Example 1 Point Slope (slope/point)
Write an equation of a line, in point-slope form, with a slope of and through the point (3, −2).
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑦+2= 1 4 (𝑥−3)

4. Writing Linear Equations: Example 2 Point Slope (slope/point)
Write an equation of a line, in point-slope form, with a slope of − 7 4 and through an x-intercept of −9.
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
x-intercept: (−9, 0)
𝑦−0=− 7 4 𝑥+9
𝑦=− 7 4 (𝑥+9)

5. Writing Linear Equations: Example 3 Point Slope (slope/point)
Write an equation of a line, in point-slope form, with a slope of and through the point (7, 2).
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑦−2= 4 3 (𝑥−7)

6. Writing Linear Equations: Example 1 Slope Intercept (slope/point)
Write an equation of a line, in slope-intercept form, with a slope of and through the point (0, 2).
Start in point slope and isolate y to transform into slope intercept
𝑦−2= 4 5 (𝑥−0)
𝑦−2= 4 5 𝑥
𝑦= 4 5 𝑥+2

7. Writing Linear Equations: Example 2 Slope Intercept (slope/point)
Write an equation of a line, in slope-intercept form, with a slope of −3 and through the point (1, −2).
𝑦+2=−3(𝑥−1)
𝑦+2=−3𝑥+3
𝑦=−3𝑥+1

8. Writing Linear Equations: Example 3 Slope Intercept (slope/point)
Write an equation of a line, in slope-intercept form, with a slope of −2 and through the point (−3, 0).
𝑦−0=−2(𝑥+3)
𝑦=−2𝑥−6

9. Writing Linear Equations: Example 1 Point Slope (2 points)
Write an equation of a line, in point slope form, through the points 2, 4 and (−1, −3).
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑚= −3−4 −1−2 =− −7 −3 = 7 3
2 options
𝑦+3= 7 3 (𝑥+1) or 𝑦−4= 7 3 (𝑥−2)

10. Writing Linear Equations: Example 2 Point Slope (2 points)
Write an equation of a line, in point-slope form, through the points (−8, 0) and (5, −1).
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑚= −1−0 5−−8 =− 1 13
2 options
𝑦−0=− 1 13 (𝑥+8) or 𝑦+1=− 1 13 (𝑥−5)

11. Writing Linear Equations: Example 3 Point Slope (2 points)
Write an equation of a line, in point-slope form, through the points (3, 1) and (2, 4).
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑚= 4−1 2−3 = 3 −1 =−3
2 options
𝑦−1=−3(𝑥−3) or 𝑦−4=−3(𝑥−2)

12. Writing Linear Equations: Example 1 Slope Intercept (2 points)
Write an equation of a line, in slope-intercept form, through the points (−4, 1) and (0, 2).
𝑚= 2−1 0−−4 = 1 4
𝑦−2= 1 4 (𝑥−0)
𝑦−2= 1 4 𝑥
𝑦= 1 4 𝑥+2

13. Writing Linear Equations: Example 2 Slope Intercept (2 points)
Write an equation of a line, in slope-intercept form, through an x-intercept of (−3, 0) and a y-intercept of (0, 6).
𝑚= 6−0 0−−3 = 6 3 =2
𝑦−0=2(𝑥+3)
𝑦=2𝑥+6

14. Writing Linear Equations: Example 3 Slope Intercept (2 points)
Write an equation of a line, in slope-intercept form, through the points (2, 2) and (−9, 6).
𝑚= 6−2 −9−2 = 4 −11
𝑦−2=− 𝑥−2
𝑦−2=− 4 11 𝑥+ 8 11
𝑦=− 4 11 𝑥