Question 188·Medium·Algebra

Pick one point to be $(x_1, y_1)$ and the other to be $(x_2, y_2)$—it does not matter which you call which, as long as you stay consistent in the formula.

Find $y_2 - y_1$ and $x_2 - x_1$ separately, being careful with subtracting negative numbers, then put them into the fraction and reduce it.

In the expression line, type (-1 - 5)/(7 - (-3)) and press Enter. Desmos will display a decimal value for this fraction.

Convert the decimal Desmos shows into a simplified fraction in your head or on paper, and then select the answer choice whose fraction is equal to that value.

For a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, the slope $m$ is given by

This is often described as "rise over run" (change in $y$ over change in $x$).

Let $(-3, 5)$ be $(x_1, y_1)$ and $(7, -1)$ be $(x_2, y_2)$.

So:

• $x_1 = -3$, $y_1 = 5$
• $x_2 = 7$, $y_2 = -1$

Use the formula parts:

• Change in $y$: $y_2 - y_1 = -1 - 5 = -6$
• Change in $x$: $x_2 - x_1 = 7 - (-3) = 7 + 3 = 10$

Now plug these into the slope formula:

Simplify $\dfrac{-6}{10}$ by dividing numerator and denominator by $2$:

So, the slope of the line is $-\dfrac{3}{5}$.