Question

NEED HELP! ASAP! 50 POINTS!

Answer 1

Answer:

$k=-8$

Step-by-step explanation:

We have the two points: (2, -3) and (k, 7).

And we want to find the value of k such that the slope between these two points is -1.

So, we can use the slope formula:

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

Let (2, -3) be (x₁, y₁) and let (k, 7) be (x₂, y₂). Let's also substitute the slope m for -1. This gives us:

$-1=\frac{7-(-3)}{k-2}$

So, let's solve for k. Add in the numerator:

$-1=\frac{10}{k-2}$

Notice that we can rewrite the left side as:

$\frac{-1}{1}=\frac{10}{k-2}$

Now, we can cross-multiply:

$-(k-2)=10$

Divide both sides by -1. This removes the negative on the left:

$k-2=-10$

Finally, add 2 to both sides. So, the value of k is:

$k=-8$

And we're done!