Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.

Step-by-step explanation:

Remember that:

We want to find the value of x such that .

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:

Subtract:

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:

Solve for x. Simplify the right:

Cross multiply:

Multiply on the right:

Divide both sides by 4:

Subtract 1 from both sides:

So, the value of x is -7.

And we're done!

step-by-step explanation: