Answer:
C. {(2,–5), (5,–9), (29,–41)}
Step-by-step explanation:
we have
[tex]y=-\frac{4}{3}x-\frac{7}{3}[/tex]
The slope of the given line is [tex]m=-\frac{4}{3}[/tex]
we know that
If a set of ordered pairs is a solution of the given line
then
the slope between two points of the set must be equal to [tex]m=-\frac{4}{3}[/tex]
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Verify each case
case A) {(3,–19), (2,3), (8,26)}
[tex]m=\frac{26-3}{8-2}[/tex]
[tex]m=\frac{23}{6}[/tex]
so
[tex]\frac{23}{6}\neq-\frac{4}{3}[/tex]
The set of case A) is not a solution of the given line
case B) {(–3,–17), (4,11), (3,19)}
[tex]m=\frac{19-11}{3-4}[/tex]
[tex]m=-8[/tex]
so
[tex]-8\neq-\frac{4}{3}[/tex]
The set of case B) is not a solution of the given line
case C) {(2,–5), (5,–9), (29,–41)}
[tex]m=\frac{-9+5}{5-2}[/tex]
[tex]m=-\frac{4}{3}[/tex]
so
[tex]-\frac{4}{3}=-\frac{4}{3}[/tex] ----> is true
Verify if the third point satisfy the equation of the given line
(29,–41)
[tex]-41=-\frac{4}{3}(29)-\frac{7}{3}[/tex]
[tex]-41*3=-123[/tex]
[tex]-123=-123[/tex] ------> is true
therefore
The set of case C) is a solution of the given line
case D) {(–2,–18), (9,–61), (5,15)}
[tex]m=\frac{15+61}{5-9}[/tex]
[tex]m=-\frac{76}{4}[/tex]
[tex]m=-19[/tex]
so
[tex]-19\neq-\frac{4}{3}[/tex]
The set of case D) is not a solution of the given line
