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romanna [79]
3 years ago
11

Problem

Mathematics
1 answer:
user100 [1]3 years ago
4 0
<h2>Answer:</h2>

<em>The slope is 3/2 and y-intercept is 5.</em>

<h2>Step-by-step explanation:</h2>

_______________________________________

The question states:

<em>Find the slope and y-intercept of the line that is perpendicular to </em>

y=-\frac{2}{3}x+5

<em>and passes through the point (-6, -4)</em>

_______________________________________

From functions, we know that if two lines, called line 1 and line 2, are perpendicular, then it is true that:

m_{1}\times m_{2}=-1 \\ \\ \\ Where: \\ \\ m_{1}: Slope \ of \ line \ 1 \\ \\ m_{2}: Slope \ of \ line \ 2

If the given line is called line 1, then:

m_{1}=-\frac{2}{3}

Then:

m_{2}=-\frac{1}{m_{1}} \\ \\ m_{2}=-\frac{1}{-\frac{2}{3}} \\ \\ \boxed{m_{2}=\frac{3}{2}}

On the other hand, the y-intercept can be found as:

y=m_{2}x+b \\ \\ y=\frac{3}{2}x+b \\ \\ For \ (x,y)=(-6,-4) \\ \\ -4=\frac{3}{2}(-6)+b \\ \\ Solving \ for \ b: \\ \\ -4=-9+b \\ \\ b=9-4 \\ \\ \boxed{b=5}

<em>Find the slope is 3/2 and y-intercept is 5.</em>

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