Greetings!
To find the slope and y-intercept of this line, we need to rearrange the equation into slope y-intercept form:
[tex] y=mx+b [/tex]
To accomplish this, let's first isolate the y variable:
[tex] -7x-4y=12 [/tex]
First, add 7x to both sides:
[tex] (-7x-4y)+(7x)=(12)+(7x) [/tex]
[tex] -4y=7x+12 [/tex]
Divide both sides of the equation by -4:
[tex] \frac{-4y}{-4}=\frac{7x+12}{-4}[/tex]
[tex] y=\frac{7}{-4}x+\frac{12}{-4} [/tex]
[tex] y=-\frac{7}{-4}x-3[/tex]
The slope (m) is equal to:
[tex]\boxed{-\frac{7}{4}}[/tex]
The y-intercept (b) is equal to:
[tex]\boxed{-3}[/tex]
I hope this helped!
-Benjamin
