we know that
A line has a slope of [tex]\frac{4}{3}[/tex]
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
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) [tex](24, 19)\ (8, 10)[/tex]
substitute in the formula
[tex]m=\frac{10-19}{8-24}[/tex]
[tex]m=\frac{-9}{-16}[/tex]
[tex]m=\frac{9}{16}[/tex]
[tex]\frac{9}{16} \neq \frac{4}{3}[/tex]
therefore
case A) is not the solution
case B) [tex](10, 8)\ (16, 0)[/tex]
substitute in the formula
[tex]m=\frac{0-8}{16-10}[/tex]
[tex]m=\frac{-8}{6}[/tex]
[tex]m=-\frac{4}{3}[/tex]
[tex]-\frac{4}{3} \neq \frac{4}{3}[/tex]
therefore
case B) is not the solution
case C) [tex](28, 10)\ (22, 2)[/tex]
substitute in the formula
[tex]m=\frac{2-10}{22-28}[/tex]
[tex]m=\frac{-8}{-6}[/tex]
[tex]m=\frac{4}{3}[/tex]
[tex]\frac{4}{3} = \frac{4}{3}[/tex]
therefore
case C) could be the solution
case D) [tex](4, 20)\ (0, 17)[/tex]
substitute in the formula
[tex]m=\frac{17-20}{0-4}[/tex]
[tex]m=\frac{-3}{-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
[tex]\frac{3}{4} \neq \frac{4}{3}[/tex]
therefore
case D) is not the solution
the answer is
The line could be through the points [tex](28, 10)\ (22, 2)[/tex]
