1. Writing Equations in Point-Slope Form
4.2
Writing Equations in Point-Slope Form
How can you write the equation of a line when you are given the slope and a point on the line?
Students will be able to write an equation of a line given its slope and a point on the line.
Students will be able to write an equation of a line given two points on the line.

2. Students will be able to write an equation of a line given its slope and a point on the line.
The point-slope form for writing an equation of a line is
𝑦=𝑚(𝑥− 𝑥 1 )+ 𝑦 1
Where, m is the slope and
( 𝑥 1 , 𝑦 1 ) is the point
Hence, the point-slope form

3. Students will be able to write an equation of a line given its slope and a point on the line.
The point-slope form for writing an equation of a line is
𝑦=𝑚(𝑥− 𝑥 1 )+ 𝑦 1
Write an equation in point-slope form of the line that passes through the point (-8,3) and has the slope of 1 4
𝑦= 𝑥− −8 +3
𝑦= 𝑥+8 +3
𝑦= 𝑥+2+3
𝑦= 𝑥+5
Point-slope form
Slope-intercept form

4. Students will be able to write an equation of a line given its slope and a point on the line.
The point-slope form for writing an equation of a line is
𝑦=𝑚(𝑥− 𝑥 1 )+ 𝑦 1
Write an equation in point-slope form of the line that passes through the point (3,-1) and has the slope of -2
𝑦=−2 𝑥− 3 +(−1)
𝑦=−2 𝑥−3 −1
𝑦=−2𝑥+6−1
𝑦=−2𝑥+5
Point-slope form
Slope-intercept form

5. You Try!!
Students will be able to write an equation of a line given its slope and a point on the line.
Write an equation in point-slope form of the line that passes through the point (4,0) and has the slope of − 2 3
𝑦=− 𝑥−4 +0
𝑦=− 𝑥−4
𝑦=− 𝑥+ 8 3
Point-slope form
Slope-intercept form

6. You Try!!
Students will be able to write an equation of a line given its slope and a point on the line.
Write an equation in point-slope form of the line that passes through the point (1,6) and has the slope of − 1 2
𝑦=− 𝑥−1 +6
𝑦=− 𝑥
𝑦=− 𝑥
Point-slope form
Slope-intercept form

7. 2. Students will be able to write an equation of a line given two points on the line.
When you are given two points on a line, you can write an equation of the line using the following steps.
Find the slope of the line.
Use the slope and one of the points to write an equation of the line in point-slope form.

8. Write an equation in slope-intercept form of the line shown.
2. Students will be able to write an equation of a line given two points on the line.
Write an equation in slope-intercept form of the line shown.
Find the slope from the graph
Slope = −4 2 =−2
2. Use the slope and the point (1,2)
𝑦=−2 𝑥−1 +2
𝑦=−2𝑥+2+2
𝑦=−2𝑥+4
Would it matter if we used the other point (3,-2)
𝑦=−2 𝑥−3 −2
𝑦=−2𝑥+6−2
rise =−4
run =2

9. 2. Students will be able to write an equation of a line given two points on the line.
Write a linear function f with the values 𝑓 4 =−2 and 𝑓 8 =4.
Note that you can rewrite 𝑓 4 =−2 as (4,-2) and 𝑓 8 =4 as (8,4)
Find the slope
(4,−2)
− (8,4)
+ (−8,−4)
−4 −6
∆𝑥 ∆𝑦
𝑚= −6 −4 = 3 2
Use the slope and a point
𝑦= 𝑥−4 −2
𝑦= 𝑥−6−2
𝑦= 𝑥−8
If we use the other point
𝑦= 𝑥−8 +4
𝑦= 𝑥−12+4
𝑦= 𝑥−8

10. You Try!!
2. Students will be able to write an equation of a line given two points on the line.
Write an equation in slope-intercept form of the line that passes through the given points.
(1,4), (3,10)
1,4
− (3,10)
(−4,−1), (8,−4)
(−4,−1)
− (8,−4)
Use the slope and a point
𝑦=3 𝑥−1 +4
𝑦=3𝑥−3+4
𝑦=3𝑥+1
+ (−3,−10)
−2 −6
∆𝑥 ∆𝑦
𝑚= −6 −2 =3
+ (−8,+4) −
∆𝑥 ∆𝑦
𝑚= 3 −12 =− 1 4
Use the slope and a point
𝑦=− 1 4 𝑥+4 −1
𝑦=− 1 4 𝑥−1−1
𝑦=− 1 4 𝑥−2

11. So let’s review!
Students will be able to write an equation of a line given its slope and a point on the line.
𝑦=𝑚(𝑥− 𝑥 1 )+ 𝑦 1
Where, m is the slope and
( 𝑥 1 , 𝑦 1 ) is the point
Hence, the point-slope form
2. Students will be able to write an equation of a line given two points on the line.
Find the slope of the line.
Use the slope and one of the points to write an equation of the line in point-slope form.