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

a. {(3,–19), (2,3), (8,26)}
b. {(–3,–17), (4,11), (3,19)}
c. {(2,–5), (5,–9), (29,–41)}
d. {(–2,–18), (9,–61), (5,15)}

C. {(2,–5), (5,–9), (29,–41)}

Step-by-step explanation:

we have

The slope of the given line is

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

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

Verify each case

case A) {(3,–19), (2,3), (8,26)}

so

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

case B) {(–3,–17), (4,11), (3,19)}

so

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

case C) {(2,–5), (5,–9), (29,–41)}

so

----> is true

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

(29,–41)

------> is true

therefore

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

case D)  {(–2,–18), (9,–61), (5,15)}

so

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