To find the equation of the line in its slope-intercept form, you can find the slope of the line and then use the point-slope formula.
The formula for the slope is
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where} \\ m\text{ is the slope of the line} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
In this case, you have
[tex]\begin{gathered} (x_1,y_1)=(0,15) \\ (x_2,y_2)=(5,0) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{0-15}{5-0} \\ m=\frac{-15}{5} \\ m=-3 \end{gathered}[/tex]
Now, the point-slope formula is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-15=-3(x-0_{}) \\ y-15=-3x-0_{} \\ \text{Add 15 to both sides of the equation} \\ y-15+15=-3x-0+15 \\ y=-3x+15 \end{gathered}[/tex]
Therefore, the equation in slope-intercept form to represent this situation is
[tex]y=-3x+15[/tex]
