MATH SOLVE

3 months ago

Q:
# What is the equation of a line that is perpendicular to (-6,3) and (3,5)

Accepted Solution

A:

The equation of the line that is perpendicular to the line passesthrough (-6 , 3) and (3 , 5) and passes through point (2 , 7) is y = [tex]-\frac{9}{2}[/tex] x + 16Step-by-step explanation:Let us explain how to find the equation of a line perpendicular to a line passes through two pointsFind the slope of the line which passes through the two given pointFind the slope of the perpendicular line by reciprocal the slope of the line which passes through the given points and change its sign because the product of the slopes of the perpendicular lines is -1Then write the equation of the line in the form y = m x + b, where m is the slope of the line and b is the y-intercept, to find the y-intercept you must have a point lies on the line The missing information is the line passes through point (2 , 7)The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line∵ A given line passes through points (-6 , 3) and (3 , 5)∴ [tex]x_{1}[/tex] = -6 and [tex]x_{2}[/tex] = 3∴ [tex]y_{1}[/tex] = 3 and [tex]y_{2}[/tex] = 5∵ The slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]- Substitute the values in the formula∵ [tex]m=\frac{5-3}{3-(-6)}[/tex]∴ [tex]m=\frac{2}{9}[/tex]To find the slope of a perpendicular line reciprocal the slope and change its sign∵ The slope of the line is [tex]\frac{2}{9}[/tex]∴ The slope of the perpendicular line to it = [tex]-\frac{9}{2}[/tex]∵ The form of the equation is y = m x + b∴ The equation of the ⊥ line is y = [tex]-\frac{9}{2}[/tex] x + b- To find b substitute x and y by the coordinates of a point lies on the line∵ The line passes through point (2 , 7)∴ 7 = [tex]-\frac{9}{2}[/tex] (2) + b∴ 7 = -9 + b- Add 9 to both sides∴ 16 = b∴ y = [tex]-\frac{9}{2}[/tex] x + 16The equation of the line that is perpendicular to the line passesthrough (-6 , 3) and (3 , 5) and passes through point (2 , 7) is y = [tex]-\frac{9}{2}[/tex] x + 16Learn more:You can learn more about perpendicular lines in brainly.com/question/11223427#LearnwithBrainly