Question

a line has slope \\(\frac{4}{3}\\). through which two points could this line pass?
a. \\((24, 19), (8, 10)\\)
b. \\((10, 8), (16, 0)\\)
c. \\((28, 10), (22, 2)\\)
d. \\((4, 20), (0, 17)\\)
please select the best answer from the choices provided
\\(\bigcirc\\) a
\\(\bigcirc\\) b
\\(\bigcirc\\) c
\\(\bigcirc\\) d

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We need to check which pair of points gives a slope of \( \frac{4}{3} \).

Step2: Check option A

For points \( (24, 19) \) and \( (8, 10) \):
\( m=\frac{10 - 19}{8 - 24}=\frac{-9}{-16}=\frac{9}{16}
eq\frac{4}{3} \).

Step3: Check option B

For points \( (10, 8) \) and \( (16, 0) \):
\( m=\frac{0 - 8}{16 - 10}=\frac{-8}{6}=-\frac{4}{3}
eq\frac{4}{3} \).

Step4: Check option C

For points \( (28, 10) \) and \( (22, 2) \):
\( m=\frac{2 - 10}{22 - 28}=\frac{-8}{-6}=\frac{4}{3} \). This matches the given slope.

Step5: Check option D (optional, but for completeness)

For points \( (4, 20) \) and \( (0, 17) \):
\( m=\frac{17 - 20}{0 - 4}=\frac{-3}{-4}=\frac{3}{4}
eq\frac{4}{3} \).

Answer:

C. \((28, 10), (22, 2)\)