Create the equation of the line

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

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Perpendicular lines have slopes which are negative reciprocals.

The slope of line kk is -5.  Therefore the slope of line jj would be 1/5.

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

Substitute the point (5,9) and the slope, 1/5, into slope-intercept form to get the y-intercept.

9 = (1/5)(5) + b  {substituted 9 in for y, 1/5 in for m, and 5 in for x}
9 = 1 + b   {multiplied 1/5 by 5}
b = 8   {subtracted 1 from each side}
y-intercept is 8

y = (1/5)x + 8 is the equation of the line  {substituted 1/5 in for slope and 8 in for y-intercept}

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