Write the equation of the line

Line k has a slope of -5.  Line j is perpendicular to line k, and passes through the point (5,9).  Create the equation for line j.

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Perpendicular lines have slopes which are negative reciprocals.

Slope of line k is -5, therefore slope of line j is 1/5.

Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

Line j slope is 1/5 and passes through the point (5,9).

Find the y-intercept of line j by substituting point and slope into slope-intercept form
y = mx + b
9 = (1/5)(5) + b   {substituted point for x and y,  and slope into slope-intercept form}
9 = 1 + b   {multiplied 1/5 by 5}
b = 8   {subtracted 1 from each side}

y = (1/5)x + 8

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