Question

Find an equation of the line that is perpendicular to the graph of 2x+5y=5 and contains the point of intersection of the graphs of y=x+4 and y–2x=5.

Answer 1

5(x+1) -2(y-3) = 0

Explanation:

For a given line ax+by=c and point (h, k), a perpendicular line through the point can be written as ...

b(x-h) -a(y-k) = 0

A graphing calculator shows the point of intersection of the graphs of the two lines to be (x, y) = (-1, 3), so the line perpendicular to 2x+5y=5 through that point can be written ...

5(x+1) -2(y-3) = 0

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In the attached graph, the requested line is shown in black.