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

Spencer and Abigail are correct

Lauren is incorrect

Explanation:

Spencer and Abigail are correct

Slope = change in y ÷ change in x

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

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

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

`\implies m=(4-(-1))/(5-3)=\frac52`

This is Spencer's method

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

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

`\implies m=(-1-4)/(3-5)=\frac52`

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

where it should have been
`m=(y_2-y_1)/(x_2-x_1)`