Write out the given equation
[tex]3x+4y=4[/tex]Make y the subject of the equation given
[tex]\begin{gathered} 3x+4y=4 \\ 3x-3x+4y=4-3x \\ 4y=4-3x \\ \frac{1}{4}\times4y=\frac{1}{4}\times4-\frac{1}{4}\times3x \\ y=1-\frac{3}{4}x \end{gathered}[/tex]Write the function of y in slope and intercept form defining the slope and intercept
[tex]\begin{gathered} y=1-\frac{3}{4}x \\ y=-\frac{3}{4}x+1=====\text{equation}(1) \\ \text{the general equation of y in slope and intercept form is} \\ y=mx+c=====\text{equation}(2) \\ \text{where m is the slope and c is the intercept} \\ \text{Combining equation 1 and 2} \\ \text{From equation 1} \\ \text{slope(m)}=-\frac{3}{4} \\ i\text{ntercept(c)}=1 \end{gathered}[/tex][tex]\begin{gathered} \text{the slope intercept form is} \\ y=-\frac{3}{4}x+1 \end{gathered}[/tex]Hence, the slope-intercept form of the question is y= (-3/4)x +1
