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Title: Finding the equation of a line given two points
Description: A lecture notes on finding the equation of a line with a short quiz.
Description: A lecture notes on finding the equation of a line with a short quiz.
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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
...
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
...
(2 , -3) and (0 , -5)
3
...
(-2 , 6) and ( -3 , 0)
5
...
1
...
3
...
5
...
1
...
y = x – 5
3
...
y = 6x + 18
5
Title: Finding the equation of a line given two points
Description: A lecture notes on finding the equation of a line with a short quiz.
Description: A lecture notes on finding the equation of a line with a short quiz.