Question

What is the equation of the line that is parallel to the given line and passes through the point (12,-2)? 12 10 8 (126) 6 Oy=-x + 10 O y=-x + 12 O y=-x-10 O y=x - 12 -10 3 6 4 22 2 4 6 8 10 12 14 x (12-2 (0 1-0 12

Answer 1

two lines are perpendicular if have the inverted slope and different sign

first find the slope of the drawn line using the formula of the slope

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \end{gathered}$

i will use the points (-2,5) and (0,-3)

$\begin{gathered} m=\frac{-3-5}{0-(-2)} \\ \\ m=-4 \end{gathered}$

the slope of the drawn line is -4 so the slope of the perpendicular line is 1/4

finding the perpendicular line

the general equation of the line is

$y=mx+b$

where m is the slope and b the y-intercept

replacing the slope m=1/4 and the point (-4,-3) i can find b

$\begin{gathered} (-3)=(\frac{1}{4})(-4)+b \\ -3=-1+b \\ b=-3+1 \\ b=-2 \end{gathered}$

the equation of the perpendicular line is

$y=\frac{1}{4}x-2$

and the point-slope form is

$(y+3)=\frac{1}{4}(x+4)$

so, the solution is the option C