We know that if two lines are Perpendicular then Product of Slopes of both of these Perpendicular lines should be Equal to -1
Given : Equation of 1st Perpendicular line is -x + 3y = 9
This can be written as :
3y = x + 9
y = x/3 + 3
Comparing with standard form : y = mx + c
we can notice that slope of 1st Perpendicular line = 1/3
Slope of 1st Line × Slope of 2nd line = -1
1/3 × Slope of 2nd line = -1
Slope of 2nd line = -3
We know that the form of line passing through point (x₀ , y₀) and having slope m is :
y - y₀ = m(x - x₀)
Here the 2nd Perpendicular line passes through the point (-3 , 2)
x₀ = -3 and y₀ = 2 and we found m = -3
⇒ y - 2 = -3(x + 3)
⇒ -3x - 9 = y - 2
⇒ -3x - y = 7
The equation of the perpendicular is [tex]\boxed{y=- 3x - 7}.[/tex]
Further explanation:
The linear equation with slope m and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The equation of the line is [tex]- x + 3y = 9[/tex] and passes through the point is [tex]\left( { - 3,2} \right).[/tex]
Explanation:
The product of the slope of perpendicular line and the slope of line is [tex]-1.[/tex]
[tex]\boxed{{m_1} \times {m_2} = - 1}[/tex]
Solve the equation [tex]- x + 3y = 9.[/tex]
[tex]\begin{aligned}- {\text{ }}x + 3y&= 9\\3y &= 9 + x\\y&= \frac{1}{3}x + \frac{9}{3}\\y&= \frac{1}{3}x+3\\\end{aligned}[/tex]
The slope of the line is [tex]{m_1} = \dfrac{1}{3}.\[/tex]
The slope of perpendicular line can be obtained as follows,
[tex]\begin{aligned}{m_1} \times {m_2}&=- 1\\\frac{1}{3} \times {m_2}&= - 1\\{m_2}&= - 3\\\end{aligned}[/tex]
The passes through the point is [tex]\left( { - 3,2} \right).[/tex]
Substitute [tex]-3[/tex] for [tex]x,[/tex] [tex]2[/tex] for [tex]y[/tex] and [tex]-3[/tex] for m in equation y = mx + c.
[tex]\begin{aligned}2&=- 3\left({- 3}\right)+ c\\2&= 9 + c\\ 2 - 9&= c\\- 7&= c\\\end{aligned}[/tex]
The equation of the perpendicular is [tex]\boxed{y =- 3x - 7}.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: equation of a line, perpendicular, -x+3y=9, passes through point, (-3,2) numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
