# Questions on slope and intercept for y = mx + c

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.