Question

The pair of points lies on the same line with the given slope. Find x.

(5, -15), (x, -21); slope = -2

a) 4
b) 6
c) 8
d) 10

Answer 1

Using the slope formula (slope = (y2 - y1) / (x2 - x1)), the value of x can be found given the slope and one pair of coordinates. By substituting the provided values and solving the equation, it is determined that x equals 8.

Step-by-step explanation:

To find the value of x for a pair of points lying on a line with a given slope, we use the formula for the slope of a line between two points, which is slope (m) = (y2 - y1) / (x2 - x1). In this case, we are provided with the slope, which is -2, and two points: (5, -15) and (x, -21). Let's solve for x using the information given.

We have the slope formula as follows:
-2 = (-21 - (-15)) / (x - 5)

This simplifies to:
-2 = (-21 + 15) / (x - 5)
-2 = -6 / (x - 5)

Now, we cross-multiply to solve for x:
-2(x - 5) = -6
-2x + 10 = -6

Adding 2x to both sides, we get:
10 = -6 + 2x
10 + 6 = 2x
16 = 2x
x = 16 / 2
x = 8

Thus, the value of x is 8, which corresponds to option (c).