Question 248·Medium·Algebra

For the point $(k+4, 2)$, which part is $x$ and which part is $y$? Do the same for $(k, -6)$ before plugging into the formula.

When you compute $x_2 - x_1$, remember that $x_1$ is $k+4$. Use parentheses: $k - (k+4)$. Do the same for $y_2 - y_1$.

After simplifying the numerator and denominator, see if negative signs cancel and if any terms with $k$ subtract to $0$.

In Desmos, type k = 0 and click the slider icon to create a slider for $k$. Then enter the two points as (k+4, 2) and (k, -6) so you can see them move as $k$ changes.

In a new line, type slope((k+4, 2), (k, -6)). Desmos will display a numeric value for this expression.

Move the $k$ slider to different values and observe that the displayed value of slope((k+4, 2), (k, -6)) does not change. That constant value is the slope of the line.

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

Let $(x_1, y_1) = (k+4, 2)$ and $(x_2, y_2) = (k, -6)$.

Substitute into the slope formula:

First simplify the numerator:

Now simplify the denominator:

So the slope becomes:

Now divide:

So, the slope of the line is $2$, which corresponds to choice D.