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,

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semsee45 semsee45 · Answer 1 · 2022-02-14T18:29:13+01:00

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 [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let [tex](x_1,y_1)[/tex] = (3, -1)

Let [tex](x_2,y_2)[/tex] = (5, 4)

[tex]\implies m=\dfrac{4-(-1)}{5-3}=\dfrac52[/tex]

This is Spencer's method

Let [tex](x_1,y_1)[/tex] = (5, 4)

Let [tex](x_2,y_2)[/tex] = (3, -1)

[tex]\implies m=\dfrac{-1-4}{3-5}=\dfrac52[/tex]

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:

[tex]m=\dfrac{y_2-y_1}{x_1-x_2}[/tex]

where it should have been [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]