Question

A line goes through the point (2, 4) and has a slope of 3/2. Which of the following points is also on the line? Circle all that apply.

A (1, 1)
B (3,7)
C (0, 2)
D (4,7)
E (0, 1)

Answer 1

The answers are D and E

Answer 2

Explanation:

We can use the point-slope form of the equation of a line to check which points lie on the line:

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

For point A (1, 1):

y - y1 = m(x - x1)

y - 1 = (3/2)(x - 2)

y - 1 = (3/2)x - 3

y = (3/2)x - 2

The point (1, 1) does not lie on the line.

For point B (3, 7):

y - y1 = m(x - x1)

y - 7 = (3/2)(x - 2)

y - 7 = (3/2)(3 - 2)

y - 7 = (3/2)

y = (3/2) + 7

y = (3/2)x + 11/2

The point (3, 7) lies on the line.

For point C (0, 2):

y - y1 = m(x - x1)

y - 2 = (3/2)(x - 2)

y - 2 = (-3/2)(2)

y = -2

The point (0, 2) does not lie on the line.

For point D (4, 7):

y - y1 = m(x - x1)

y - 7 = (3/2)(x - 2)

y - 7 = (3/2)(4 - 2)

y - 7 = 3

y = 10

The point (4, 7) does not lie on the line.

For point E (0, 1):

y - y1 = m(x - x1)

y - 1 = (3/2)(x - 2)

y - 1 = (-3/2)(2)

y = -2

The point (0, 1) does not lie on the line.

Therefore, the point (3, 7) is the only point that lies on the line. Answer: B