Find an equation of the line through the point and perpendicular to the line .

Question

Find an equation of the line through the point  and perpendicular to the line  .

Quizplus · Accepted Answer

To find the slope of the line perpendicular to the given line, we take the negative reciprocal of the slope:
m = -(1/3) --> slope of perpendicular line
Now we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the given point.
Plugging in the values, we get:
y - (-4) = -(1/3)(x - 7)
Simplifying and converting to the standard form gives us:
3y + x = 5

Find an Equation of the Line Through the Point