Question

Simone claims that the slope of the line through (-2, 7) and (3, 0) is the same as the slope of the line through (2, 1) and (12, -13) is simone's claim true or false

Answer 1

Simone is correct

Explanation:

Given

Line 1:

`(x_1,y_1) = (-2, 7)`

`(x_2,y_2) = (3, 0)`

Line 2:

`(x_1,y_1) = (2, 1)`

`(x_2,y_2) =(12, -13)`

Required

Is Simone correct?

Slope (m) is calculated using:

`m = (y_2 - y_1)/(x_2 - x_1)`

For Line 1

`m = (0 - 7)/(3 - (-2))`

`m = (0 - 7)/(3 +2)`

`m = (-7)/(5)`

`m = -(7)/(5)`

For Line 2:

`m = (-13 - 1)/(12 -2)`

`m = (-14)/(10)`

Divide by 2/2

`m = (-14/2)/(10/2)`

`m = (-7)/(5)`

`m = -(7)/(5)`

By comparison, both lines have the same slope.

Hence, Simone is correct