Question

a line goes through the point (5, -7) and has slope m = -3. write the equation that represents the line.

Answer 1

We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

`(y-y_1)=m(x_{}-x_1)`

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

`\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}`

Therefore, the equation of the line in slope-intercept form is

`y=-3x+8`