Answered

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Write an equation of the line in slope intercept form that is is perpendicular to the equation y = -5x + 1 through the point (2,-1)?

Sagot :

ANSWER

[tex]y=\frac{1}{5}x-\frac{7}{5}[/tex]

EXPLANATION

We want to find the equation of the line that is perpendicular to the given line:

[tex]y=-5x+1[/tex]

First, we have to find the slope of the line. The slope of a line perpendicular to a given line is the negative inverse of the slope of the line.

The slope of the given line is -5.

Therefore, the slope of the perpendicular line is:

[tex]\begin{gathered} m=-(\frac{1}{-5}) \\ m=\frac{1}{5} \end{gathered}[/tex]

To find the equation of the line, we have to apply the point-slope method:

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

where (x1, y1) is the point the line passes through.

Therefore, the equation of the line is:

[tex]\begin{gathered} y-(-1)=\frac{1}{5}(x-2) \\ y+1=\frac{1}{5}x-\frac{2}{5} \\ y=\frac{1}{5}x-\frac{2}{5}-1 \\ y=\frac{1}{5}x-\frac{7}{5} \end{gathered}[/tex]

That is the equation of the line.

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