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.
First, let's find the slope of line j. Since line j is perpendicular to line k, the slope of line j will be the negative reciprocal of the slope of line k.
The slope of line k is -5, so the slope of line j is the reciprocal of -5, which is 1/5.
Using the point-slope form of a linear equation, the equation for line j can be written as:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the point (5,9) and m is the slope 1/5.
Plugging in the values, we get:
y - 9 = 1/5(x - 5)
Simplifying, we have:
y - 9 = 1/5x - 1
Moving the -9 to the other side, we get:
y = 1/5x - 1 + 9
Simplifying further:
y = 1/5x + 8