Question

I need help part two and three of this question:A line passes through the following points: (6,3) and (2,9)1. Write the equation of the lineWhich I got y=-3/2 x+122. Write an equation of a line that is perpendicular to the original form. 3. Write the equation of a line that is parallel to the original form.

Answer 1

Part 2:

To determine an equation that is perpendicular to the line equation y = -3/2x + 12, get the negative reciprocal of the slope of the line equation.

`\begin{gathered} \text{Given slope: }m=-(3)/(2) \\ \\ \text{The negative reciprocal is} \\ -\Big(-(3)/(2)\Big)^(-1)=(2)/(3) \\ \\ \text{We can now assume that any line in the form} \\ y=(2)/(3)x+b \\ \text{where }b\text{ is the y-intercept} \\ \text{is perpendicular to the line }y=-(3)/(2)x+12 \end{gathered}`

Part 3:

An equation that is parallel to the line y = -3/2x + 12, is a line equation that will have the same slope as the original line.

Given that the slope of the line is m = -3/2, then any line equation in the form

`\begin{gathered} y=-(3)/(2)x+b \\ \text{where} \\ b\text{ is the y-intercept} \end{gathered}`