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)

Explanation:

Step1: Find slope of given line

The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For \((3,4)\) and \((-2,2)\), \( m=\frac{2 - 4}{-2 - 3}=\frac{-2}{-5}=\frac{2}{5} \). Parallel lines have equal slopes.

Step2: Check slope of (-2,-5) and (-7,-3)

Slope \( m_1=\frac{-3 - (-5)}{-7 - (-2)}=\frac{2}{-5}=-\frac{2}{5}
eq \frac{2}{5} \).

Step3: Check slope of (-1,1) and (-6,-1)

Slope \( m_2=\frac{-1 - 1}{-6 - (-1)}=\frac{-2}{-5}=\frac{2}{5} \). Equal to given slope.

Step4: Check slope of (0,0) and (2,5)

Slope \( m_3=\frac{5 - 0}{2 - 0}=\frac{5}{2}
eq \frac{2}{5} \).

Step5: Check slope of (1,0) and (6,2)

Slope \( m_4=\frac{2 - 0}{6 - 1}=\frac{2}{5} \). Equal to given slope.

Step6: Check slope of (3,0) and (8,2)

Slope \( m_5=\frac{2 - 0}{8 - 3}=\frac{2}{5} \). Equal to given slope.

Answer:

(-1, 1) and (-6, -1), (1, 0) and (6, 2), (3, 0) and (8, 2)