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Write the slope -intercept form of the equation of the line that passes through the point (2, 4) , and is perpendicular to y = - x + 5 . 5 points

Answer :

The given equation is

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

This equation shows a slope of -1, which a perpendicular line would have a slope of 1 because perpendicular slopes are opposite and reciprocal as 1 and -1 are.

Then, we use the point-slope formula to find the equation

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

Where,

[tex]\begin{gathered} m=1 \\ x_1=2 \\ y_1=4 \end{gathered}[/tex][tex]\begin{gathered} y-4=1(x-2) \\ y=x-2+4 \\ y=x+2 \end{gathered}[/tex]

Hence, the new perpendicular line is y = x + 2.

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