Question

Please help. The point P(4, 28) lies on the curve y = x² + x + 8. If Q is the point (x, x² + x + 8), find the

slope of the secant line PQ for the following values of x.

Answer 1

Hope it helps you with something.

Explanation:

The slope of the secant line PQ passing through points P(4, 28) and Q(x, x² + x + 8) can be found using the formula:

slope of PQ = (change in y) / (change in x) = [(y₂ - y₁) / (x₂ - x₁)]

where (x₁, y₁) = (4, 28) and (x₂, y₂) = (x, x² + x + 8).

Substituting the values, we get:

slope of PQ = [(x² + x + 8 - 28) / (x - 4)]

simplifying, we get:

slope of PQ = [(x² + x - 20) / (x - 4)]

Now, we can find the slope of PQ for different values of x:

When x = 2:

slope of PQ = [(2² + 2 - 20) / (2 - 4)] = [(-14) / (-2)] = 7

Therefore, the slope of PQ when x = 2 is 7.

When x = 3:

slope of PQ = [(3² + 3 - 20) / (3 - 4)] = [(-14) / (-1)] = 14

Therefore, the slope of PQ when x = 3 is 14.

Hence, the slope of the secant line PQ for x = 2 is 7, and for x = 3 is 14.