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.
