Question

WORTH 50 POINTSSS

Answer 1

The equation of the perpendicular is $\boxed{y=- 3x - 7}.$

Further explanation:

The linear equation with slope m and intercept $c$ is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Given:

The equation of the line is $- x + 3y = 9$ and passes through the point is $\left( { - 3,2} \right).$

Explanation:

The product of the slope of perpendicular line and the slope of line is $-1.$

$\boxed{{m_1} \times {m_2} = - 1}$

Solve the equation $- x + 3y = 9.$

$\begin{aligned}- {\text{ }}x + 3y&= 9\\3y &= 9 + x\\y&= \frac{1}{3}x + \frac{9}{3}\\y&= \frac{1}{3}x+3\\\end{aligned}$

The slope of the line is ${m_1} = \dfrac{1}{3}.$

The slope of perpendicular line can be obtained as follows,

$\begin{aligned}{m_1} \times {m_2}&=- 1\\\frac{1}{3} \times {m_2}&= - 1\\{m_2}&= - 3\\\end{aligned}$

The passes through the point is $\left( { - 3,2} \right).$

Substitute $-3$ for $x,$ $2$ for $y$ and $-3$ for m in equation y = mx + c.

$\begin{aligned}2&=- 3\left({- 3}\right)+ c\\2&= 9 + c\\ 2 - 9&= c\\- 7&= c\\\end{aligned}$

The equation of the perpendicular is $\boxed{y =- 3x - 7}.$

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 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.

Answer 2

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