Answer:
[tex]k=-8[/tex]
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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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:
[tex]-1=\frac{7-(-3)}{k-2}[/tex]
So, let's solve for k. Add in the numerator:
[tex]-1=\frac{10}{k-2}[/tex]
Notice that we can rewrite the left side as:
[tex]\frac{-1}{1}=\frac{10}{k-2}[/tex]
Now, we can cross-multiply:
[tex]-(k-2)=10[/tex]
Divide both sides by -1. This removes the negative on the left:
[tex]k-2=-10[/tex]
Finally, add 2 to both sides. So, the value of k is:
[tex]k=-8[/tex]
And we're done!
