Answer :
Hello there. To solve this question, we'll have to remember some properties about the equation of a line.
Given the equation:
[tex]4x+3y=12[/tex]We have to determine the slope and the y-intercept of this line.
For this, the best way to start is to find the equation of the line in slope-intercept form. It is given by:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
To do so, we simply have to solve the equation for y.
Start subtracting 4x on both sides of the equation:
[tex]\begin{gathered} 4x+3y-4x=12-4x \\ 3y=12-4x \end{gathered}[/tex]Divide both sides of the equation by a factor of 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{12-4x}{3} \\ \\ y=4-\frac{4}{3}x \end{gathered}[/tex]Comparing it to the slope-intercept form of the line, we find that:
[tex]\begin{gathered} m=-\frac{4}{3} \\ b=4 \end{gathered}[/tex]These are the slope and the y-intercept of the equation.