Question

Mark and Luisa are finding the slope of the line through (2,4) and (-1,5).

Who is correct? Explain your reasoning.

Short answer

Luisa is correct.

Step-by-step solution

Step 1- Given information

A pair of points $(2,4),(-1,5)$.

Step 2- Formula used

The slope formula of a line is:

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

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{and}{x}_1\ne x_2.$

Step 3- To find the slope 

Here, $(x_1,y_1)=(2,4){\text{and (x}}_2,y_2)=(-1,5)$

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

$\begin{array}{l}\Rightarrow m=\frac{5-4}{-1-2}\\ \Rightarrow m=-\frac{1}{3}\end{array}$

Therefore, the slope of the line is $-\frac{1}{3}$.

Hence, the Luisa is correct.