Question

Find the slope and intercept of the given equation $y = - 8x + 2$ ?

Answer 1

Hint: In this question we are given a line whose equation is $y = - 8x + 2$ and we have been asked to find out its slope and intercept. We can simply find the slope and intercept of the given equation $y = - 8x + 2$ by substituting the values in the given formula.

Formula used: For any equation \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] ,
Slope (m) = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
To find intercept,
y-intercept = \[\dfrac{{ - {\text{C}}}}{{\text{B}}}\]

Complete step-by-step solution:
First, we have to find the slope of the given equation $y = - 8x + 2$ ,
We all know that, for any equation \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] , the formula for slope is given by:
Slope (m) = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
For this, we have to compare the given equation $y = - 8x + 2$ and \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] .
Then, change the given equation in the form of \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] to find the values of ${\text{A,B and C}}$ .
That is, in $y = - 8x + 2$ , ${\text{y}}$ should be transferred to the right hand side. And the equation becomes
$ - 8x - y + 2 = 0$ .
So here we get,
$Ax = - 8x$ , \[By = - y\] , $C = 2$
Now as we know the Slope (m) of the line = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$ .
Therefore, the slope of $ - 8x - y + 2 = 0$ is $\dfrac{{ - {\text{A}}}}{{\text{B}}}$ .
$ = - \dfrac{{ - 8}}{{ - 1}} = - 8$
Slope (m) = $ - 8$
Now, to find the intercept of $y = - 8x + 2$ , we have to use the formula of y-intercept,
y-intercept = \[\dfrac{{ - {\text{C}}}}{{\text{B}}}\]
As we know,
$Ax = - 8x$ , \[By = - y\] , $C = 2$ , $m = - 8$
Therefore, by using the formula we get,
y-intercept = \[\dfrac{{ - {\text{C}}}}{{\text{B}}}\]
y-intercept = \[\dfrac{{ - 2}}{{ - 1}}\]
y-intercept = \[2\]

Hence the slope and y- intercept of the given equation $y = - 8x + 2$ is slope (m)$ = - 8$ and y- Intercept\[ = 2\]

Note: Alternative method:
This is an alternative method to find the y-intercept,
The equation of slope intercept form is $y = mx + b$ , where ${\text{m}}$ is the slope of the line and $b$ is the y-intercept.
Now, the equation is$ - 8x - y + 2 = 0$, we have to change this in the form of $y = mx + b$
$ - 8x - y + 2 = 0$
Rearranging it we get,
$y = - 8x + 2$
$y = - 8x + 2$ , which is now in the form of $y = mx + b$
Therefore, the intercept of the given equation $y = - 8x + 2$ is y- intercept = $b = 2$.