Question

How do you find the slope intercept form of the equation of the line with y-intercept $(0, - 2)$ and x-intercept $(8,0)$ ?

Answer 1

Hint : To solve this problem we should know about the slope of a line.
Slope: The slope of line is the steepness of a line. It rises over the run, the change in ‘y’ over the change in ‘x’.
Slope of line, $m = \dfrac{{rise}}{{run}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
The slope intercept form of a linear equation is $y = mx + b$
Here, $b$ is my intercept value.

Complete step by step solution:
First of all we have to calculate the slope of the line as two points given in the problem.
As slope of line, $m = \dfrac{{rise}}{{run}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
By keeping value in it. We get,
$m = \dfrac{{0 - ( - 2)}}{{8 - 0}}$
$\Rightarrow m = \dfrac{{0 + 2}}{{8 - 0}} = \dfrac{2}{8} = \dfrac{1}{4}$
As we know the slope intercept form of a linear equation is $y = mx + b$
By putting the value of $m$ as we had calculated from above and value of y-intercept from the question. We get,
$y = \dfrac{1}{4}x + ( - 2)$
$\Rightarrow y = \dfrac{1}{4}x - 2$
By further simplification. We get,
$\Rightarrow 4y = x - 8$
Hence, the slope intercept form of the equation of the line with y-intercept $(0, - 2)$ and x-intercept $(8,0)$ is $4y = x - 8$ .
So, the correct answer is “ $4y = x - 8$ ”.

Note : There is some general rules relating to slope that is:
A line is increasing if it goes up from left to right. The slope is positive, i.e. $m > 0$ .
A line is decreasing if it goes down from right to left. The slope is positive, i.e. $m < 0$ .
If the line is horizontal the slope is zero. i.e. $m = 0$ .
If the line is vertical then slope is undefined.