Question

Use the given conditions to write an equation for the line in point-slope form and general form.Passing through (-5,9) and parallel to the line whose equation is 3x-2y-7=0...

Answer 1

First, we need to find the slope of the given line to which our unknown line is parallel. Remember, parallel lines have equal slopes!

`\begin{gathered} 3x-2y-7=0 \\ \\ -2y=-3x+7 \\ \\ y=(3)/(2)x-(7)/(2) \end{gathered}`

By writing the equation in slope-intercept form, we find the slope to be 3/2. We will use this and the given point (-5, 9) to solve the equation of the unknown line.

So, the equation of the line in point-slope form is:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-9=(3)/(2)(x+5) \end{gathered}`

In general form, the equation is:

`\begin{gathered} y-9=(3)/(2)(x+5) \\ \\ 2y-18=3(x+5) \\ 2y-18=3x+15 \\ -3x+2y-33=0 \\ 3x-2y+33=0 \end{gathered}`