Given below are the set of questions related to finding the value of slope and x – y intercept for the equation y = mx + c.

In previous lessons, we have already discussed the formula for slope and intercept for y = mx + c.

**Slope of line = m **

**x intercept = -c / m****y intercept = c**

I hope you remember the above formulas. Let us solve some problems related to the concept.

## Solved problems on slope and intercept

**Example 01**

Find slope and intercept of below equation.

2x + 5y + 6 = 0

**Solution**

Representing the equation in form of y = mx + c

\mathtt{2x\ +\ 5y\ +\ 6\ =\ 0}\\\ \\ \mathtt{5y\ =\ -2x\ -\ 6}\\\ \\ \mathtt{y\ =\ \frac{-2}{5} x-\frac{6}{5}}

On comparing the expression, we get;

m = -2/5

c = -6/5

**Slope of equation = m = -2/5****x – intercept** = -c/m = – (-6/5) ÷(-2/5) = -3

**y intercept** = c = -6/5

Given below is the graph of above equation.

**Example 02**

Find slope and intercept of equation.

y – 6x + 7 = 0

**Solution**

Arranging the equation in form of y = mx + c

y – 6x + 7 = 0

y = 6x – 7

Comparing the equation with y = mx + c, we get following values;

m = 6

c = -7

**Slope of line = m = 6**

**X intercept** = -c / m = – (-7) / 6 = 7/6

**Y intercept** = c = -7

Given below is the graph of given equation.

**Example 03**

Find the slope and intercept of following equations.

4y + 16 = 0

**Solution**

Representing the equation in form of y = mx + c

\mathtt{4y\ +\ 16\ =\ 0}\\\ \\ \mathtt{4y\ =\ -16}\\\ \\ \mathtt{y\ =\ -4}\\\ \\ \mathtt{y\ =\ 0.x\ -\ 4}

Comparing the equation with y = mx + c, we get;

m = 0

c = -4

**Slope of line** = m = 0**x – intercept** = -c / m = – (-4)/0 = Not applicable

**y intercept** = c = -4

Given below is the graph of above equation.

**Example 04**

Find the slope and intercept of below equation

8x – 4y – 20 = 0

**Solution**

Represent the above equation on form of y = mx + c

\mathtt{8x-\ 4y\ -\ 20\ =\ 0}\\\ \\ \mathtt{4y\ =\ 8x\ -\ 20}\\\ \\ \mathtt{y\ =\ 2x\ -\ 5}

Comparing the equation with y = mx + c, we get following;

m = 2

c = -5**Slope of equation** = m = 2**x intercept** = -c/m = – (-5)/2 = 5/2

**y intercept** = c = -5

Given below is the graph of given equation.

**Example 05**

Find the slope and intercept of below equation.

x – 15 = 0

**Solution**

Representing the equation in form of y = mx + c

x – 15 = 0

0.y = x – 15

On comparing the equation we get;

m = 1 and c = -15

**Slope of equation** = m = 1**x intercept** = -c /m = – (-15)/1 = 15

**y intercept** = Not applicable since coefficient of ” Y ” is zero

Given below is the graph of x – 15 = 0

**Example 06**

The line passes through point (-8, 2) and (-7, -1). Find the slope and intercept of the line.

**Solution**

Let the equation of line be y = mx + c.

Since the line passed through (-8,2), it will satisfy the equation.

y = mx + c

2 = -8m + c – – eq (1)

Similarly point (-7, 1) will also satisfy the equation.

y = mx + c

1 = -7m + c – – eq (2)

Solving both the equations;

So, we get **m = -1**.

Putting the value of m in one of the above equation.

1 = -7m + c

1 = -7(-1) + c

c = -6

So we get both the values of m and c. Now calculating the slope and intercept gets easier.

Slope of line = m = -1

x – intercept = -c / m = – (-6) / (-1) = -6

y intercept = c = -6

Given below is the graph of required line.