Question

Find the equation (in terms of x ) of the line through the points (-2,-5) (3,0)

Answer 1

First, find the slope of the line using the given two points (-2,5) and (3,0)

`\begin{gathered} \text{Let} \\ (x_1,y_1)=(-2,5) \\ (x_2,y_2)=(3,0) \\ \\ m = (y_2 - y_1)/(x_2 - x_1) \\ m=(0-5)/(3-(-2)) \\ m=(-5)/(3+2) \\ m=(-5)/(5) \\ m=-1 \end{gathered}`

Now that we have the slope, solve for the equation using the point-slope form, in this instance we will use (-2,5)

`\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-5=-1\lparen x-(-2)) \\ y-5=-x-2 \\ x=-y-2+5 \\ x=-y+3 \end{gathered}`

The equation therefore (in terms of x) is x = -y + 3.