1. Point-Slope Form & Graphing
Lesson 36

2. Objectives
HSF-LE.2: Construct linear functions given a graph, description of a relationship, or two input-output pairs.

3. Point-Slope Form of an Equation
Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form.
Recall
1) 𝑥 1 , 𝑦 1 is a point on the graph
2) m = slope

4. Example; Find an equation of the line
Write the equation of the line in point-slope form and in slope-intercept form with slope –5 through (1, 3).
Point-Slope Form
Slope-Intercept form.
y – 3 = –5(x – 1)
y – y1 = m(x – x1)
y – 3 = –5x + 5
y – (3) = –5(x – 1)
Substitute.
Distribute.
y = –5x + 8
Solve for y.
y – 3 = –5(x – 1)
Simplify.
y - 3= -5(x – 1)
y = -5x + 8

5. Example; Find an equation of the line
Write the equation of the line in slope-intercept form through (–2, –3) and (2, 5).
Use points:
(-2, -3) and (2, 5)
m = 𝒚 𝟏 − 𝒚 𝟐 𝒙 𝟏 − 𝒙 𝟐
= 𝟓−−𝟑 𝟐−−𝟐
= 𝟖 𝟒
= 𝟐
Point-Slope Form
Slope-Intercept form.
y – 5 = 2(x - 2)
y – y1 = m(x – x1)
y – 5 = 2x - 4
Distribute.
y – (5) = 2(x – 2)
Substitute.
y = 2x + 1
Solve for y.
y – 5 = 2(x – 2)
Simplify.
y - 5= 2(x – 2)
y = 2x + 1

6. Example; Graph the line
𝑦− 4 =− 2 3 𝑥− −3
y 1
𝑥 1
Slope
m = − 2 3
Point = (-3, 4)

7. Example; Graph the line
𝑦− −1 = 1 3 𝑥− 3
y 1
𝑥 1
Slope
m = 1 3
Point = (3, -1)

8. #36: Point-Slope Form & Graphing
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