Question

How do you graph using the intercept for $ x - 2y = 8 $ ?

Answer 1

Hint: We have given an equation of a line as $ x - 2y = 8 $ , which is a straight-line equation. A straight-line equation is always linear and represented as $ y = mx + c $ where $ m $ is the slope of the line and $ c $ is the y-intercept and $ \dfrac{{ - c}}{m} $ is the x-intercept

Complete step-by-step answer:
We have equation of line,
  $
  x - 2y = 8 \\
  or \\
  y = \dfrac{1}{2}x - \dfrac{8}{2} \\
   \Rightarrow y = \dfrac{1}{2}x - 4 \;
  $
Now we compare this given equation with the general linear equation i.e., $ y = mx + c $
Hence ,
Slope of the given line, $ m = \dfrac{1}{2} $ .
y-intercept of the given line , $ c = - 4 $ .
Therefore, we can say that point $ (0, - 4) $ lies on the line.
x-intercept of the given line , $ \dfrac{{ - c}}{m} = \dfrac{{ - ( - 4)}}{{\dfrac{1}{2}}} = 8 $ .
Therefore, we can say that point $ (8,0) $ lies on the line.
With the help of two points, we can plot the graph by connecting the points as follow,

Note: This type of linear equations sometimes called slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allows us to graph it.
We can quickly tell the slope i.e., $ m $ the y-intercepts i.e., $ (y,0) $ and the x-intercept i.e., $ (0,y) $ .we can graph the corresponding line .