Question

A line has a slope of 4/3. Through which two points could this line pass?

Answer 1

The answer to this is C. (28,10) and (22,2).

Answer 2

we know that

A line has a slope of $\frac{4}{3}$

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we will proceed to calculate the slope in each case and compare with the slope of the given line to determine the solution

case A) $(24, 19)\ (8, 10)$

substitute in the formula

$m=\frac{10-19}{8-24}$

$m=\frac{-9}{-16}$

$m=\frac{9}{16}$

$\frac{9}{16} \neq \frac{4}{3}$

therefore

case A) is not the solution    

case B) $(10, 8)\ (16, 0)$

substitute in the formula

$m=\frac{0-8}{16-10}$

$m=\frac{-8}{6}$

$m=-\frac{4}{3}$

$-\frac{4}{3} \neq \frac{4}{3}$

therefore

case B) is not the solution    

case C) $(28, 10)\ (22, 2)$

substitute in the formula

$m=\frac{2-10}{22-28}$

$m=\frac{-8}{-6}$

$m=\frac{4}{3}$

$\frac{4}{3} = \frac{4}{3}$

therefore

case C) could be the solution    

case D) $(4, 20)\ (0, 17)$

substitute in the formula

$m=\frac{17-20}{0-4}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

$\frac{3}{4} \neq \frac{4}{3}$

therefore

case D) is not the solution  

the answer is

The line could be through the points $(28, 10)\ (22, 2)$