Mathematics: 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

Simone claims that the slope of the line through

kristofwr3444

08.02.2022

Simone is correct

Step-by-step 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:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For Line 1

$m = \frac{0 - 7}{3 - (-2)}$

$m = \frac{0 - 7}{3 +2}$

$m = \frac{-7}{5}$

$m = -\frac{7}{5}$

For Line 2:

$m = \frac{-13 - 1}{12 -2}$

$m = \frac{-14}{10}$

Divide by 2/2

$m = \frac{-14/2}{10/2}$

$m = \frac{-7}{5}$

$m = -\frac{7}{5}$

By comparison, both lines have the same slope.

Hence, Simone is correct

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