Question

NEED HELP! ASAP! 50 POINTS!

Find the value of k so that the line through the given points has the given slope.

(2,-3) and (k,7) m= -1

Answer 1

`k=-8`

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=(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=(7-(-3))/(k-2)`

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

`-1=(10)/(k-2)`

Notice that we can rewrite the left side as:

`(-1)/(1)=(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!