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.