Question

patty and tim are asked to find the slope of the line that passes through the points (4,3) and (7,9). is either of them correct? explain. patty: $m=\frac{9 - 3}{7 - 4}=\frac{6}{3}=2$. tim: $m=\frac{7 - 4}{9 - 3}=\frac{3}{6}=\frac{1}{2}$

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify the points

Let $(x_1,y_1)=(4,3)$ and $(x_2,y_2)=(7,9)$.

Step3: Calculate the slope

Substitute the values into the formula: $m=\frac{9 - 3}{7 - 4}=\frac{6}{3}=2$.

Step4: Analyze Patty and Tim's work

Patty calculated $m=\frac{9 - 3}{7 - 4}=\frac{6}{3}=2$ correctly. Tim made a mistake in the order of subtraction in the denominator. He calculated $m=\frac{7 - 4}{9 - 3}=\frac{3}{6}=\frac{1}{2}$, but the correct formula requires subtracting the $x$ - coordinates in the same order as the $y$ - coordinates.

Answer:

Patty is correct. The slope of the line passing through the points $(4,3)$ and $(7,9)$ is 2. Tim is incorrect because he did not use the correct order of subtraction in the slope - formula.