y = mx + c is called the slope-intercept form equation of the straight line. In this article, we are going to learn more details about the y = mx + c graph of the straight line. In y = mx + c, m represents the slope value of the equation and c is the y-intercept. The graph y = mx + c cuts the y-axis at the point p the OP is the y-intercept of the graph and O is the origin.
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y-intercept of y = mx + c
The general form of the equation of the straight line is y = mx + c where m is slope or gradient and c is the y-intercept that cuts the y-axis at some point c. It is a linear equation and the variables x and y are the coordinates on the plane. x, y are independent and dependent variables respectively. The y-intercept of the line that is on the graph y = mx + c is c.
Slope y = mx+c Formula
The equation y = mx + c is derived from the slope formula.
m = (y-c)/(x-0)
m = (y-c)/x
mx = y – c
mx + c = y
y = mx + c
Thus the slope-intercept form of the equation of the line is derived.
How to find the y-intercept of Equation of Straight Line y = mx + c?
- To find the y-intercept of the line y = mx + c we have to rearrange the equation to make y the subject.
- Substitute x = 0 into the equation to find the y-intercept.
- Declare the coefficient of x.
Slope Intercept Form of Equation y = mx + c Examples
Example 1.
What is the y-intercept of the graph of 6x + 2y = 3?
Solution:
Given that the equation is 6x + 2y = 3
2y = -6x + 3
y = – 6/2x + 3/2
y = -3x + 3/2
We know that
y = mx + c,
Comparing the equation with y = mx + c
we get c = 3/2. So, the y-intercept = 3/2
Example 2.
What is the y-intercept of the graph of x + y = 3?
Solution:
Given that the equation is 7x + 2y = 3
y = -x + 3
y = – x + 3
y = -x + 3
We know that
y = mx + c,
Comparing the equation with y = mx + c
we get c = 3. So, the y-intercept = 3
Example 3.
What is the y intercept of the graph of 5y = 2x + 3
Solution:
Given that the equation is 5y = 2x + 3
y = 2/5x + 3/5
We know that
y = mx + c
Comparing the equation with y = mx + c
We get c = 3/5
Therefore the y-intercept = 3/5
Example 4.
What is the y-intercept of the graph of 4x + 2y = 6?
Solution:
Given that the equation is 4x + 2y = 6
4x + 2y – 6 = 0
2y = -4x + 6
y = – 4/2x + 6/2
y = -2x + 3
We know that
y = mx + c,
Comparing the equation with y = mx + c
we get c = 3. So, the y-intercept = 3
Example 5.
What is the y-intercept of the graph of 7x + 8y = 26?
Solution:
Given that the equation is 7x + 8y = 26
8y = -7x + 26
y = – 7/8x + 26/8
y = -7/8x + 13/4
We know that
y = mx + c,
Comparing the equation with y = mx + c
we get c = 13/4. So, the y-intercept = 13/4
FAQs on y-intercept of the Graph of y = mx + c
1. What is y = mx + c?
The expression y = mx + c is an equation of a line
Here m is the slope of the line and the y-intercept of c.
This equation is formed by knowing the slope of the line and the intercept which the line cuts on the y-axis. This equation y = mx + c is the basic equation of the line.
2. How to use y = mx + c?
- To find the y-intercept of the line y = mx + c we have to rearrange the equation to make y the subject.
- Substitute x = 0 into the equation to find the y-intercept.
- Declare the coefficient of x.
3. What is the y-intercept of the graph 5x + 2y = 5?
5x + 2y = 5
2y = -5x + 5
y = -5/2 x + 5/2
Now compare the equation with y = mx + c
c = 5/2 so, the y-intercept = 5/2.