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October 16, 2019
Finding Equation of a Line Given Two Points
Learning Objective/s:
A
...
Find the equation of a line given two points
C
...
In this equation, x and y are
coordinates of a point, m is the slope, and b is the y-coordinate of the y-intercept
...


Method 1
To find the equation of a line given two points (x₁ , y₁) and (x₂ ,
y₂) on the line, use the Two Point Form
y - y₁ =

𝑦2 −𝑦₁
𝑥2 −𝑥₁

(x - x₁)

(x1, y1) are the coordinates of the first point
(x2, y2) are the coordinates of the second point

Example 1:
Find the equation of the line given the points (1, 2) and (3, 8) in y = mx + b
Solution:
First, identify the values of (x₁, y₁) and ( x₂,y₂) in (1, 2) and (3, 8)
...
Express
equation in slope intercept form
...
Express
equation in slope intercept form
Solution:
x₁ = 8

y₁ = 3

x₂ = 10

y₂ = 4

𝑦 2 −𝑦₁

y - y₁ = 𝑥 2 −𝑥₁ (x - x₁)
4−3

y – 8 = 10−8 ( x – 8 )

Substitution the values of x₁ , y₁ , x₂ and y₂

1

y–8=2(x–8)
y–8=

𝑥
2

−

Simplify

8

Multiply ½ with x – 8

2

y–8=½x–4
2

y–8+8=½x–4+8

Add 8 to both sides of the equation then
simplify

y=½x+4

Equation of the line

Method 2
Step 1: Find the slope of the line using m =

𝒚𝟐 −𝒚₁
𝒙𝟐 −𝒙₁

Step 2: Find the y-intercept (b) by substituting the value of slope (m)
and choose one point (x,y) in the slope intercept form
...
Use y = mx + b, substitute the value of
slope (m) and y-intercept (b)
...

Identify the values of (x₁, y₁) and ( x₂,y₂) in (1, 2) and (3, 8)
x₁ = 1 y₁ = 2

x₂ = 3 y₂ = 8

Step 1: Solve for slope
𝑦 2 −𝑦₁

8 −2

6

m = 𝑥 2 −𝑥₁ = 3 −1 = 2 = 3

Substitute the values in the formula and
simplify

Slope or m = 3
Step 2:
Use y = mx + b (slope intercept form) to find the y-intercept
...


Example 6:
Find the equation of the line passing through the points (2, 4) and (5, 10)
...

x₁ = 2 y₁ = 4
Step 1: Use m =
𝑦 2 −𝑦₁
𝑥 2 −𝑥₁

=

x₂ = 5 y₂ = 10

𝒚𝟐 −𝒚₁
𝒙𝟐 −𝒙₁

10 −4
5 −2

to solve for slope

6

=3=2

Substitute the values in the formula and simplify

Slope or m = 2
Step 2:
Use the slope intercept form to find the y-intercept
...


4

Quiz
QUARTER ___1st___/ SEMESTER _________

A
...
Identify the following statement if it is true then draw
then draw

and if it is false


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The equation of the line given m = 2 and (3,-4) is y = 2x+2
...
The equation of the line given (-1,5) and (2,17) is y = 4x+9
...
To obtain the equation y = -4x, the given slope should be -4 and y-intercept is 0
...
Given m = -8 and (0,6), the equation will be y = -8x – 2
...
If the given slope is 1 and the y-intercept is 0, then the equation will be y = 1
...
Find the equation of the line given the following:

Given

Equation

1
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(2 , -3) and (0 , -5)
3
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(-2 , 6) and ( -3 , 0)
5
...

1
...

3
...

5
...

1
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y = x – 5
3
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y = 6x + 18
5

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