Question

8. A line passes through the polnts (-1, 4) and (2,-2). What is the equation of this line? 9. A line with a slope of 2 passes through the point (2. 1). What is the equation of this line?

Answer 1

8.

`\begin{gathered} \text{let:} \\ (x1,y1)=(-1,4) \\ (x2,y2)=(2,-2) \\ \text{the slope is:} \\ m=(y2-y1)/(x2-x1)=(-2-4)/(2-(-1))=(-6)/(3)=-2 \end{gathered}`

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-4=-2(x-(-1)) \\ y=-2x+2 \end{gathered}`

9.

`\begin{gathered} \text{let:} \\ (x1,y1)=(2,1) \\ m=2 \end{gathered}`

Using the slope-point equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-1=2(x-2) \\ y=2x-3 \end{gathered}`