Question

Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (–2, 2)? Check all that apply. (–2, –5) and (–7, –3) (–1, 1) and (–6, –1) (0, 0) and (2, 5) (1, 0) and (6, 2) (3, 0) and (8, 2)

Answer 1

Answer:-The required ordered pairs are (–1,1) and (–6,–1),(0, 0) and (2, 5)  and (3, 0) and (8, 2).

Explanation:-

We know that parallel lines have equal slopes.

Slope of line that contains (3,4) and (-2,2)= $\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{-2-3}=\frac{2}{5}$

Given options are:-

1. Slope of line that contains (–2,–5) and (–7,–3)= $\frac{-3-(-5)}{-7-(-2)}=\frac{-2}{5}$
2. Slope of line that contains (–1,1) and (–6,–1) = $\frac{-1-1}{-6-(-1)}=\frac{2}{5}$
3. Slope of line that contains (0, 0) and (2, 5)= $\frac{0-5}{0-2}=\frac{5}{2}$
4. Slope of line that contains (1,0) and (6,2) = $\frac{2-0}{6-1}=\frac{2}{5}$
5. Slope of line that contains (3, 0) and (8, 2)= $\frac{2-0}{8-3}=\frac{2}{5}$

We can see Slope of line contains (–1,1) and (–6,–1), Slope of line that contains (0, 0) and (2, 5) and Slope of line that contains (3, 0) and (8, 2) have same slope as the given line.

Thus the required ordered pairs are (–1,1) and (–6,–1),(0, 0) and (2, 5)  and (3, 0) and (8, 2).

Answer 2

Answer:

B. (–1, 1) and (–6, –1)

D. (1, 0) and (6, 2)

E. (3, 0) and (8, 2)