Finding the Y-Intercept of a Line
Math Class
Understanding the Y-Intercept
The y-intercept of a line is the point where the line crosses the
y-axis.
y
(0, 3)
x
At this point:
▶ The x-coordinate is always 0
▶ The y -coordinate is the constant term when the equation is in
slope-intercept form (y = mx + b)
Given Equation
We have the equation of line L:
2y = −5x + 6
To find the y-intercept, we need to:
1. Solve for y to get the slope-intercept form
2. Identify the constant term (b)
Step 1: Convert to Slope-Intercept Form
Starting with:
2y = −5x + 6
Divide both sides by 2:
y=
−5x + 6
2
5
y =− x +3
2
Now we have the slope-intercept form:
y = mx + b
where:
▶ m = − 52 (slope)
▶ b = 3 (y-intercept)
Identifying the Y-Intercept
From the slope-intercept form:
5
y =− x +3
2
The y-intercept is:
▶ x-coordinate: 0 (always)
▶ y -coordinate: 3 (the constant term)
Therefore, the y-intercept is at the point:
(0, 3)
Original Question
Line L has the equation 2y = −5x + 6.
Draw a ring around the coordinates of the y-intercept of line L.
1. (0, 6)
2. (0, 2)
(0, 3)
3. ○
The correct answer is (0,
○ 3).
Exercises - Find the Y-Intercept (Part 1)
Find the y-intercept for each equation:
1. y = 3x + 4
2. 2y = 6x + 8
3. y = −2x + 5
4. 3y = 9x − 6
5. y = 12 x − 7
6. 4y = −8x + 12
7. y = 5x
Exercises - Find the Y-Intercept (Part 2)
Find the y-intercept for each equation:
1. y = −x + 9
2. 5y = 10x + 15
3. y = 34 x − 2
4. 2y = 3x + 10
5. y = 7
6. 3y = −6x + 9
7. y = 4x − 1
Exercises - Find the Y-Intercept (Part 3)
Find the y-intercept for each equation:
1. y = −3x − 8
2. 4y = 12x + 20
3. y = 25 x + 6
4. 3y = x + 9
5. y = −2
6. 5y = −15x + 25
7. y = 0.5x + 1.2
Exercises - Multiple Choice (Part 4)
For each equation, circle the correct y-intercept:
1. y = 2x + 3
(0,2) (0,3) (0,-3)
2. 3y = 6x − 9
(0,3) (0,-3) (0,-9)
3. y = −x + 4
(0,4) (0,-4) (0,-1)
4. 2y = 8x + 10
(0,8) (0,5) (0,10)
5. y = 7x
(0,7) (0,0) (0,1)
6. 5y = −10x + 20
7. y = 13 x − 2
(0,4) (0,-4) (0,20)
(0,3) (0,-2) (0, 13 )
0
