We are given the following equation
[tex]4y-3x=4[/tex]We are asked to write the equation in slope-intercept from
Recall that slope-intercept is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
So let us convert the given equation into the slope-intercept form by solving for y.
[tex]4y-3x=4[/tex]Add 3x on both sides of the equation
[tex]\begin{gathered} 4y-3x+3x=3x+4 \\ 4y=3x+4 \end{gathered}[/tex]Divide both sides of the equation by 4.
[tex]\begin{gathered} \frac{4y}{4}=\frac{3}{4}x+\frac{4}{4} \\ y=\frac{3}{4}x+1 \end{gathered}[/tex]The slope is 3/4 and the y-intercept is 1
Therefore, the slope-intercept form of the given equation is
[tex]y=\frac{3}{4}x+1[/tex]