Question

coordinate geometry. use the graph to answer the questions. multiple answer 2 points. choose all that apply. the point (-1, 4) lies on the line that is parallel to the given line. what other points lie on the parallel line. (1, 3) ( - 5, 6) (0, 7) (3, 2) (3, 5)

Explanation:

Step1: Find slope of parallel line

Parallel lines have equal slopes. Since no information about the given line's slope is provided in - text, we assume the slope - formula approach. The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let the given point be $(-1,4)$ and a test point $(x,y)$.

Step2: Check each option

For point $(1,3)$: $m=\frac{3 - 4}{1-(-1)}=\frac{-1}{2}=-\frac{1}{2}$
For point $(-5,6)$: $m=\frac{6 - 4}{-5-(-1)}=\frac{2}{-4}=-\frac{1}{2}$
For point $(0,7)$: $m=\frac{7 - 4}{0-(-1)}=\frac{3}{1}=3$
For point $(3,2)$: $m=\frac{2 - 4}{3-(-1)}=\frac{-2}{4}=-\frac{1}{2}$
For point $(3,5)$: $m=\frac{5 - 4}{3-(-1)}=\frac{1}{4}$

Answer:

A. $(1,3)$
B. $(-5,6)$
D. $(3,2)$