Question

Abigail and Spencer calculate the slope of the line between the points (3,-1) and (5,4) in different ways. Abigail calculates the slope by dividing -1 - 4 with 3 - 5. Spencer divides 4 - (-1) by 5 - 3. When they check their work with their mutual friend Lauren, she says that they are both wrong and shows them her work. She calculates -1 - 4 and divides by 5 - 3. Who is correct among these three friends? Who is incorrect? Why? One of them is Spencer,

Answer 1

Answer:

Spencer and Abigail are correct

Lauren is incorrect

Step-by-step explanation:

Spencer and Abigail are correct

Slope = change in y ÷ change in x

Or  $m=\dfrac{y_2-y_1}{x_2-x_1}$

Let $(x_1,y_1)$ = (3, -1)

Let $(x_2,y_2)$ = (5, 4)

$\implies m=\dfrac{4-(-1)}{5-3}=\dfrac52$

This is Spencer's method

Let $(x_1,y_1)$ = (5, 4)

Let $(x_2,y_2)$ = (3, -1)

$\implies m=\dfrac{-1-4}{3-5}=\dfrac52$

This is Abigail's method

It doesn't matter which point you label as point 1 and point 2, as long as you carry out the slope calculation correctly.

Lauren's calculation is wrong as she calculated her slope as:

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

where it should have been $m=\dfrac{y_2-y_1}{x_2-x_1}$