Question

How do you graph using the slope and intercept of $ 4x-2y=48 $ ?

Answer 1

Hint: 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. In the given question, we have given an equation of a line as $ 4x-2y=48 $ , which is a straight-line equation. In order to draw a graph of the given equation, first we will rewrite the given equation in a slope intercept form i.e. y = mx + c. Later we will get the value of the slope and the y-intercept and the value of the x-intercept. Now, getting the points we can easily plot the graph of the given straight line equation.

Complete step-by-step answer:
We have given equation of line,
  $ 4x-2y=48 $
Rewrite the above equation in a slope intercept form, i.e. $ y=mx+c $
 $ y=2x-24 $
Now we compare this given equation with the general linear equation i.e., $ y=mx+c $
Hence ,
Slope of the given line, $ m=2 $ .
y-intercept of the given line , $ c=-24 $ .
Therefore, we can say that point $ (0,-24) $ lies on the line.
x-intercept of the given line , $ \dfrac{-c}{m}=\dfrac{-\left( -24 \right)}{2}=12 $ .
Therefore, we can say that point $ (12,0) $ lie on the line.
With the help of two points, we can plot the graph by connecting the points as follow,

Hence, this is the required graph of the given equation of line.


Note: While solving these types of questions, students need to remember that they always need to convert the given straight line equation into slope-intercept form so that by calculating we can easily find the slope and the intercepts of the given straight line. The must know about the concept of slope intercept form of equation. Slope intercept form is a form of writing an equation of a straight line. While we write any equation in this form, we usually get the values of slope and the intercept of the given straight line. This type of linear equation is sometimes called a slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allows us to graph it.
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 $ .
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.