Question

Select the four points that appear on the line with the given slope and y-intercept

Slope: 2/3 y-intercept = -9

A- (2,3)
B- (0,-9)
C- (1,9)
D-(9,-3)
E-(6,-5)
F-(3,-7)

Answer 1

The four points that appear on the line are:

B- (0,-9)

D-(9,-3)

E-(6,-5)

F-(3,-7)

Explanation:

The equation of the line in slope-intercept form is:

y = mx + b

Being m the slope and b the y-intercept.

We are given the values of m=2/3 and b=-9, so the equation of the line is:

y = 2/3 x - 9

We must select from the list below the points that lie on the line. To test each point, we substitute the value of x and calculate the value of y. If it matches the given y-coordinate, then the point lies on the line.

• A- (2,3)

Calculate: y = 2/3 (2) - 9 = -23/3.

This point is not on the line because -23/3 ≠ 3

• B- (0,-9)

Calculate: y = 2/3 (0) - 9 = -9.

This point is on the line because -9 = -9

• C- (1,9)

Calculate: y = 2/3 (1) - 9 = -25/3.

This point is not on the line, because -25/3 ≠ 3

• D-(9,-3)

Calculate: y = 2/3 (9) - 9 = -3.

This point is on the line because -3 = -3

• E-(6,-5)

Calculate: y = 2/3 (6) - 9 = -5.

This point is on the line because -5 = -5

• F-(3,-7)

Calculate: y = 2/3 (3) - 9 = -7.

This point is on the line because -7 = -7

The four points that appear on the line are:

B- (0,-9)

D-(9,-3)

E-(6,-5)

F-(3,-7)