Question

Write an equation in slope intercept form to represent this situation

Answer 1

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

`\begin{gathered} m=(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}`

In this case, you have

`\begin{gathered} (x_1,y_1)=(0,15) \\ (x_2,y_2)=(5,0) \\ m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(0-15)/(5-0) \\ m=(-15)/(5) \\ m=-3 \end{gathered}`

Now, the point-slope formula is

`\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}`

Therefore, the equation in slope-intercept form to represent this situation​ is

`y=-3x+15`