Question

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

A. (24, 19), (8, 10)

B. (10, 8), (16, 0)

C. (28, 10), (22, 2)

D. (4, 20), (0, 17)

Answer 1

we know that

A line has a slope of
`(4)/(3)`

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

`m=(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=(10-19)/(8-24)`

`m=(-9)/(-16)`

`m=(9)/(16)`

`(9)/(16) \\eq (4)/(3)`

therefore

case A) is not the solution

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

substitute in the formula

`m=(0-8)/(16-10)`

`m=(-8)/(6)`

`m=-(4)/(3)`

`-(4)/(3) \\eq (4)/(3)`

therefore

case B) is not the solution

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

substitute in the formula

`m=(2-10)/(22-28)`

`m=(-8)/(-6)`

`m=(4)/(3)`

`(4)/(3) = (4)/(3)`

therefore

case C) could be the solution

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

substitute in the formula

`m=(17-20)/(0-4)`

`m=(-3)/(-4)`

`m=(3)/(4)`

`(3)/(4) \\eq (4)/(3)`

therefore

case D) is not the solution

the answer is

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