Question

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

Explanation:

Step1: Find slope of line $p$

Identify two points on line $p$, e.g., $(0, 2)$ and $(5, -2)$. Calculate slope:
$$m = \frac{-2 - 2}{5 - 0} = -\frac{4}{5}$$

Step2: Parallel lines have equal slope

The line through $W$ has slope $-\frac{4}{5}$. Point $W$ is $(1, 5)$.

Step3: Apply point-slope formula

Point-slope form: $y - y_1 = m(x - x_1)$, substitute $x_1=1, y_1=5, m=-\frac{4}{5}$:
$$y - 5 = -\frac{4}{5}(x - 1)$$

Answer:

A. $y - 5 = -\frac{4}{5}(x - 1)$