Question

A line passes through the point (–2, 7) and has a slope of –5.

What is the value of a if the point (a, 2) is also on the line?
A.–7
B.–1
C.1
D.7

Answer 1

B

Explanation:

Let's create an equation in point-slope form, which is:
`y-y_1=m(x-x_1)`, where
`(x_1,y_1)` is the point and m is the slope.

Here, our point is (-2, 7) and our slope is m = -5 so plug these in:

`y -7=-5*(x-(-2))`

`y -7=-5*(x+2)`

Now, if (a, 2) lies on this line, then it should satisfy the equation. So plug in a for x and 2 for y:

2 - 7 = -5(a + 2)

-5 = -5(a + 2)

Divide by -5:

1 = a + 2

Subtract 2 from both sides:

a = -1

Thus, the answer is B.

Hope this helps!

Answer 2

B. -1

Explanation:

Slope = (y2 - y1)/(x2 - x1)

-5 = (7 - 2)/(-2 - a)

-5(-2 - a) = 5

10 + 5a = 5

5a = -5

a = -1