Write the equation of a line that is perpendicular to y=2/7x +9 and that passes through the point (4,-6).

Answers

Answer 1

Answer:

[tex]y=-\frac{7}{2}x+8[/tex]

Step-by-step explanation:

Given the equation

[tex]y\:=\:\frac{2}{7}x+9[/tex]

comparing the equation with the slope-intercept form

[tex]y =mx+b[/tex]            

Here,

m is the slope y is the intercept

so the slope of the line is 2/7

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

the slope of the perpendicular line will be: -7/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (4,-6) is:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-6\right)=\frac{-7}{2}\left(x-4\right)[/tex]

[tex]y+6=\frac{-7}{2}\left(x-4\right)[/tex]

[tex]y+6-6=\frac{-7}{2}\left(x-4\right)-6[/tex]

[tex]y=-\frac{7}{2}x+8[/tex]


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Answers

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Step-by-step explanation:

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