The slope is 3/2 and y-intercept is 5.
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The question states:
Find the slope and y-intercept of the line that is perpendicular to
[tex]y=-\frac{2}{3}x+5[/tex]
and passes through the point (-6, -4)
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From functions, we know that if two lines, called line 1 and line 2, are perpendicular, then it is true that:
[tex]m_{1}\times m_{2}=-1 \\ \\ \\ Where: \\ \\ m_{1}: Slope \ of \ line \ 1 \\ \\ m_{2}: Slope \ of \ line \ 2[/tex]
If the given line is called line 1, then:
[tex]m_{1}=-\frac{2}{3}[/tex]
Then:
[tex]m_{2}=-\frac{1}{m_{1}} \\ \\ m_{2}=-\frac{1}{-\frac{2}{3}} \\ \\ \boxed{m_{2}=\frac{3}{2}}[/tex]
On the other hand, the y-intercept can be found as:
[tex]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}[/tex]
Find the slope is 3/2 and y-intercept is 5.
