Question

Write a linear equation in point-slope form for the line that goes through (1,-3) and (3,9).

Answer 1

To find the linear equation that passes through two given points, we forst need to calculate the slope using the following formula:

`\begin{gathered} m=(rise)/(run) \\ \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`

So, the slope of the line that passes through (1, -3) and (3, 9) is:

`\begin{gathered} m=(9-(-3))/(3-1) \\ \\ m=(12)/(2) \\ \\ m=6 \end{gathered}`

Using the point-slope form, the equation of the line is:

`\begin{gathered} (y-y_1)=m(x-x_1) \\ \\ (y+3)=6(x-1) \\ \\ or \\ \\ (y-9)=6(x-3) \end{gathered}`

The answers are options A and B.