Question

examine the graph below. select the solutions to the graph from the following points. select three that apply.

Answer 1

Options (1), (2), (3)

Explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Given line on the graph is passing through two points (-3, 0) and (0, 1).

Slope of this line will be,

m =
`(y_2-y_1)/(x_2-x_1)`

=
`(1-0)/(0+3)`

=
`(1)/(3)`

y-intercept of the line 'b' = 1

Equation of the line will be,

y =
`(1)/(3)x+1`

If the points given in the options satisfy the equation, they will be the solution of the line.

Option (1),

For (3, 2),

2 =
`(3)/(3)+1`

2 = 2

True.

(3, 2) is the solution.

Option (2)

For (21, 8),

8 =
`(21)/(3)+1`

8 = 8

True.

(21, 8) is the solution.

Option(3)

For (-15, -4),

-4 =
`(-15)/(3)+1`

-4 = -4

True.

(-15, -4) is the solution.

Option (4)

For (12, 9)

9 =
`(12)/(3)+1`

9 = 5

False

(12, 9) is not the solution.

Option (5)

For (-6, 1)

1 =
`(-6)/(3)+1`

1 = -1

False

(-6, 1) is not the solution.

Therefore, Options (1), (2), (3) are the solutions.