Question

write an equation in slope-intercept form of the line having the given slope that contains the given point.

Answer 1

As a first step we are going to calculte the slope of CX:

C(0,3) and X(2, -1)

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(-1-3)/(2-0) \\ m=-(4)/(2) \\ m=-2 \end{gathered}`

Slope of a perpendicular line is the negative reciprocal of the original line, in this case the line that passes through T(0, -2) has a slope of -(-1/2)=1/2

So, by the slope-point form of the equation, we can get the equation in slope-intercept form:

`\begin{gathered} y-y_0=m(x-x_0) \\ y+2=(1)/(2)(x-0) \\ y=(1)/(2)x-2\text{ -> Slope-intercept form} \end{gathered}`