We have to graph the equation 4y=5x+20 using the intercepts.
First we are going to find the y-intercept of the line, to do this we have to remember that the line intercepts the y-axis when x=0. Plugging this value of x in the equation we have
[tex]\begin{gathered} 4y=5(0)+20 \\ 4y=20 \\ y=\frac{20}{4} \\ y=5 \end{gathered}[/tex]
Hence the y-intercept is 5. This represents the point (0,5).
Now we draw this point on the graph:
Now we have to find the x-intercept of the line, this happens when y=0. Plugging this value of y in the equation we have that
[tex]\begin{gathered} 4(0)=5x+20 \\ 0=5x+20 \\ 5x=-20 \\ x=-\frac{20}{5} \\ x=-4 \end{gathered}[/tex]
Then, the x-intercept is -4. This represents the point (-4,0).
Drawing this point on the graph we have.
Now we only connect the points with a straight line:
That's the graph of the line that we find with the intercepts.
