We want the line passing through the point (1,-5) that is perpendicular to the line y=-2x+5.

If two lines are perpendicular, then their slopes are opposite reciprocals of each other. Thus the slope of the line we are seeking is `1/2` .

We now a point on the line and its slope. We use the point-slope form:

`y-y_1=m(x-x_1)` where `(x_1,y_1)` is the given point and m is the slope.

Thus the equation of the line is `y-(-5)=1/2(x-1)` or `y+5=1/2(x-1)` .-------------------------------------------------------------------

**In slope-intercept form the equation of the line is `y=1/2x-11/2` **

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(The lines do not appear perpendicular due to the scale.)

**Further Reading**