Question

How do you graph using the slope and the intercept of \[x-3y=-13\]?

Answer 1

Hint: We have given an equation of a line as \[x-3y=-13\] , 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-3y=-13 $
Rewrite the equation in a slope intercept form,
 $ y=\dfrac{1}{3}x+\dfrac{13}{3} $
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}{3} $ .
y-intercept of the given line , $ c=\dfrac{13}{3}=4.33 $
Therefore, we can say that point $ (0,4.33) $ lie on the line.
x-intercept of the given line , $ \dfrac{-c}{m}=\dfrac{-\dfrac{13}{3}}{\dfrac{1}{3}}=-\dfrac{13}{3}\times \dfrac{3}{1}=-13 $ .
Therefore, we can say that point $ (-13,0) $ lie on the line.
With the help of two points, we can plot the graph by connecting the points as follow,

Note: Slope of a line can also be found if two points on the line are given. Let the two points on the line be $ ({{x}_{1}},{{y}_{1}}),({{x}_{2}},{{y}_{2}}) $ respectively.
Then slope is given by , $ m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} $ .
Slope is also defined as the ratio of change in $ y $ over the change in $ x $ between any two points.
 y-intercept can also be found by substituting $ x=0 $ .
Similarly, x-intercept can also be found by substituting $ y=0 $ .