Question

which equation best represents the point - slope form of the line that passes through point w and is parallel to line p?
$y - 5=\frac{4}{5}(x - 1)$
$y - 5=-\frac{5}{4}(x - 1)$
$y - 5=-\frac{4}{5}(x - 1)$
$y - 5=\frac{5}{4}(x - 1)$

Explanation:

Step1: Find the slope of line $p$

Pick two points on line $p$, say $(- 2,-2)$ and $(2,3)$. Using the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m=\frac{3+2}{2 + 2}=\frac{5}{4}$.

Step2: Recall the property of parallel lines

Parallel lines have the same slope. The line we want to find is parallel to line $p$, so its slope $m=\frac{5}{4}$.

Step3: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Given point $W(1,5)$, substituting $m = \frac{5}{4}$, $x_1=1$ and $y_1 = 5$ into the formula, we get $y - 5=\frac{5}{4}(x - 1)$.

Answer:

$y - 5=\frac{5}{4}(x - 1)$ (the fourth option)