Question

Given points $P(-2,7)$ and $Q(4,y)$ in a coordinate plane, for what value of $y$ is the slope of the line through $P$ and $Q$ equal to $\frac{-3}{2}$?

a) 9
b) 6
c) -5
d) -4

Answer 1

For the slope -3/2 of the line through points P(-2,7) and Q(4,y), the value of y should be -2. However, this answer is not listed in the given options, suggesting an error in the question.

Step-by-step explanation:

To find the value of y for which the slope of the line through points P(-2,7) and Q(4,y) is -\frac{3}{2}, we use the formula for slope (m):

m = \frac{y_2 - y_1}{x_2 - x_1}

Here, point P is (-2, 7) and point Q is (4, y). So, we get:

m = \frac{y - 7}{4 - (-2)} = \frac{y - 7}{6}

Since m is given as -\frac{3}{2},

-\frac{3}{2} = \frac{y - 7}{6}

Cross-multiplying gives us:

-3 \cdot 6 = 2(y - 7)

-18 = 2y - 14

Adding 14 to both sides results in:

-4 = 2y

Dividing both sides by 2, we find:

y = -2

Therefore, for the given slope, the value of y must be -2, which is not an option among the choices provided. There seems to be an error in the choices given in the question.