The slope intercept form is [tex]y=-\frac{-3x}{4}-1[/tex].
Solution:
Given data: slope = [tex]-\frac{3}{4}[/tex] and y-intercept = –1
y-intercept means (x, y) = (0, –1)
Equation of a line for slope intercept form: [tex]y-y_1=m(x-x_1)[/tex]
Here, [tex]x_1=0, y_1=-1[/tex] and [tex]m=-\frac{3}{4}[/tex].
⇒ [tex]y-(-1)=\frac{-3}{4} (x-0)[/tex]
⇒ [tex]y+1=\frac{-3}{4} (x)[/tex]
Do cross multiplication.
⇒ [tex]4(y+1)=-3x[/tex]
⇒ [tex]4y+4=-3x[/tex]
⇒ [tex]4y=-3x-4[/tex]
Divide both sides of the equation by 4.
⇒ [tex]y=-\frac{-3x}{4}-\frac{4}{4}[/tex]
⇒ [tex]y=-\frac{-3x}{4}-1[/tex]
Hence the slope intercept form is [tex]y=-\frac{-3x}{4}-1[/tex].
