Question

Which set of points contains the solutions to the equation y = –4⁄3x – 7⁄3?

Answer 1

Answer:

C. {(2,–5), (5,–9), (29,–41)}

Step-by-step explanation:

we have

$y=-\frac{4}{3}x-\frac{7}{3}$

The slope of the given line is $m=-\frac{4}{3}$

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

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

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

Verify each case

case A) {(3,–19), (2,3), (8,26)}

$m=\frac{26-3}{8-2}$

$m=\frac{23}{6}$

so

$\frac{23}{6}\neq-\frac{4}{3}$

The set of case A) is not a solution of the given line

case B) {(–3,–17), (4,11), (3,19)}

$m=\frac{19-11}{3-4}$

$m=-8$

so

$-8\neq-\frac{4}{3}$

The set of case B) is not a solution of the given line

case C) {(2,–5), (5,–9), (29,–41)}

$m=\frac{-9+5}{5-2}$

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

so

$-\frac{4}{3}=-\frac{4}{3}$ ----> is true

Verify if the third point satisfy the equation of the given line

(29,–41)

$-41=-\frac{4}{3}(29)-\frac{7}{3}$

$-41*3=-123$

$-123=-123$ ------> is true

therefore

The set of case C) is a solution of the given line

case D)  {(–2,–18), (9,–61), (5,15)}

$m=\frac{15+61}{5-9}$

$m=-\frac{76}{4}$

$m=-19$

so

$-19\neq-\frac{4}{3}$

The set of case D) is not a solution of the given line