MATH SOLVE

3 months ago

Q:
# The given line passes through the points and (-4, -3) and (4, 1).What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

Accepted Solution

A:

Answer:The equation of the line is y - 3 = -2(x + 4)Step-by-step explanation:* Lets explain how to solve the problem- The slope of the line which passes through the points (x1 , y1) and (x2 , y2) is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]- The product of the slopes of the perpendicular lines = -1- That means if the slope of a line is m then the slope of the perpendicular line to this line is -1/m- The point-slope of the equation is [tex]y - y_{1}=m(x - x_{1})[/tex]* lets solve the problem∵ A given line passes through points (-4 , -3) and (4 , 1)∴ x1 = -4 , x2 = 4 and y1 = -3 , y2 = 1∴ The slope of the line [tex]m=\frac{1-(-3)}{4-(-4)}=\frac{1+3}{4+4}=\frac{4}{8}=\frac{1}{2}[/tex]- The slope of the line perpendicular to this line is -1/m∵ m = 1/2∴ The slope of the perpendicular line is -2- Lets find the equation of the line whose slope is -2 and passes through point (-4 , 3)∵ x1 = -4 , y1 = 3∵ m = -2∵ y - y1 = m(x - x1)∴ y - 3 = -2(x - (-4))∴ y - 3 = -2(x + 4)* The equation of the line is y - 3 = -2(x + 4)