Respuesta :
The equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
According to the information given in the exercise, the y-intercept is:
[tex]b=-4[/tex]And the x-intercept is 5.
So you know that the line passes through these points:
[tex](5,0);(0,-4)[/tex]Then, you can find the slope of the line with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you can set up that:
[tex]\begin{gathered} y_2=-4_{} \\ y_1=0 \\ x_2=0 \\ x_1=5 \end{gathered}[/tex]Then, substituting values into the formula, you get that the slope is:
[tex]\begin{gathered} m=\frac{-4-0}{0-5} \\ \\ m=\frac{-4}{-5} \\ \\ m=\frac{4}{5} \end{gathered}[/tex]Knowing the values of "m" and "b", you can determine that the equation of this line in Slope-Intercept form, is:
[tex]y=\frac{4}{5}x-4[/tex]The answer is:
[tex]y=\frac{4}{5}x-4[/tex]