Question

what is the equation of the line that passes through the point (1,1) and has a slope of -5?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(1,1)$ and $m=-5$.
Substitute values: $y - 1 = -5(x - 1)$

Step2: Simplify to slope-intercept form

Expand the right side: $y - 1 = -5x + 5$
Add 1 to both sides: $y = -5x + 6$

Answer:

$y = -5x + 6$