Answer:
The linear equation [tex]4x - 9y = 36[/tex] in the slope-intercept form of the linear/line equation is:
[tex]y=\frac{4}{9}x-4[/tex]
Step-by-step explanation:
The slope-intercept form of the linear/line equation
[tex]y = mx+b[/tex]
where
- [tex]m[/tex] is the slope
- [tex]b[/tex] is the y-intercept
The given equation is
[tex]4x - 9y = 36[/tex]
Let us convert the equation in the slope-intercept form of the linear/line equation
[tex]4x - 9y = 36[/tex]
Add -4x to both sides
[tex]4x - 9y+(-4x)=36+(-4x)[/tex]
[tex]4x-9y-4x = 36-4x[/tex]
simplify
[tex]-9y=-4x+36[/tex]
Divide both sides by -9
[tex]\frac{-9y}{-9}=\frac{-4x+36}{-9}[/tex]
simplify
[tex]y=\frac{4}{9}x-4[/tex]
Therefore, the linear equation [tex]4x - 9y = 36[/tex] in the slope-intercept form of the linear/line equation is:
[tex]y=\frac{4}{9}x-4[/tex]
Further Examining the equation:
As we have already converted the given equation in the slope-intercept form such as
[tex]y=\frac{4}{9}x-4[/tex]
We can further examine the equation by comparing it with the slope-intercept form of the linear/line equation such as
[tex]y = mx+b[/tex]
Thus, by comparing with the slope-intercept form of the linear/line equation,
- The slope of the equation is: [tex]m=\frac{4}{9}[/tex]
- The y-intercept b of the equation is: [tex]b = -4[/tex]
The graph of the equation is also attached below for further understanding.
