Question

How do you graph using slope and intercept form $ 4x-y=6 $ ?

Answer 1

Hint: In the given question, we have been asked to draw a graph using the slope and intercept form of the equation. We have given an equation of a line as $ 4x-y=6 $ , 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.
Formula used:
The equation of the line in the slope and intercept form is given by;
 $ 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 solution:
We have equation of line,
 $ 4x-y=6 $
Subtracting $ 4x $ from both the sides of the equation,
 $ -y=-4x+6 $
Taking the negative sign both the sides of the equation, we will get
 $ y=4x-6 $
Now we compare this given equation with the general linear equation i.e., $ y=mx+c $
Hence,
Slope of the given line, $ m=4 $ .
y-intercept of the given line , $ c=-6 $ .
Therefore, we can say that point $ (0,-6) $ lies on the line.
x-intercept of the given line , $ \dfrac{-c}{m}=-\dfrac{-6}{4}=\dfrac{3}{2} $ .
Therefore, we can say that point $ (\dfrac{3}{2},0) $ lies 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 $ .
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) $ . And then we can graph the corresponding line by connecting the two lines.