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.