Question

write the equation of the line in point slope form of the line that is perpendicular to the given line and that passes through the given point. the write the equation in slope intercept form. y= -1/2x +3 (6,4) point-slope form: slope-intercept form:

Answer 1

when 2 lines are perpendicular its slopes are inverted and have a different sign

so, the slope of the given equation is -1/2 and the perpendicular is

$-\frac{1}{2}\longrightarrow2$

now to write the new equation we start from the general equation of the line

$y=mx+b$

where m is the slope and b the y-intercept

we replace the slope on the equation and the given point to find b

$\begin{gathered} (4)=(2)(6)+b \\ 4=12+b \\ b=4-14 \\ b=-8 \end{gathered}$

now replacing b and m we can find the equation of the perpendicular line

$y=2x-8$