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.

  5(x+1) -2(y-3) = 0

Step-by-step 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

_____

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

-6 + 3 = 3 - 6