Question

What is the equation in the slope intercept form of the line that passes through the point (3,8) and is perpendicular to the line represented by y= -3/4 x-2

Answer 1

the line is perpendicular to the line:

`y=-(3)/(4)x-2`

this means that the slope of the line will be the negative reciproc of the other line so it would be:

`m=(4)/(3)`

now with the slope and the coordinate (3,8) we can find the intersection with the y axis by replacing x = 0 so

`\begin{gathered} y-y_1=m(x-x_1) \\ y-8=(4)/(3)(0-3) \end{gathered}`

and we solve for y

`\begin{gathered} y=-4+8 \\ y=4 \end{gathered}`

So finally we can write the general equation like:

`y=(4)/(3)x+4`

where m = 4/3 and c = 4