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strojnjashka [21]
3 years ago
11

How do you graph a function? for ex: f(x)=-2x-2

Mathematics
1 answer:
torisob [31]3 years ago
6 0
It is going to be linear the slope is -2 and the y-intercept is -2
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What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?
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The equation of line that is perpendicular to the line -x+3y =9  and passes through the point \left({-3,2}\right)  is \boxed{{\mathbf{y=-3x-7}}} .

Further explanation:

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

Rewrite the given equation -x+3y =9  as follows:

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

Now, compare the obtained equation of line y=\frac{1}{3}x+3  with the standard equation of line y=mx+b .

\begin{aligned}m&=\frac{1}{3}\\b&=3\\\end{aligned}

Therefore, the slope is \frac{1}{3} .

It is given that both lines are perpendicular to each other so the product of slope must be equal to -1 .

{m_1}\cdot {m_2}=-1                                                          …… (1)

Substitute \frac{1}{3}  for {m_1}  in equation (1) to obtain the value of slope {m_2} .

\begin{aligned}\frac{1}{3}\cdot{m_2}&=-1\\{m_2}&=-3\\\end{aligned}

Therefore, the slope is -3 .

It is given that the line passes through point \left({-3,2}\right) .

The point-slope form of the equation of a line with slope m  passes through point \left({{x_1},{y_1}}\right) is represented as follows:

y-{y_1}=m\left({x-{x_1}}\right)                                      …… (2)

Substitute -3  for {x_1} , 2  for {y_1}  and -3  for m  in equation (2) to obtain the equation of line.

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

Therefore, the equation of line is y=-3x-7 .

Thus, the equation of line that is perpendicular to the line -x+3y=9  and passes through the point \left({-3,2}\right)  is \boxed{{\mathbf{y=-3x-7}}} .

Learn more:

1. Which classification best describes the following system of equations? <u>brainly.com/question/9045597 </u>

2. What is the value of x  in the equation x-y=30  when y=15 ? <u>brainly.com/question/3965451 </u>

3. What are the values of x? <u>brainly.com/question/2093003</u>

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.

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