Question

The graph of a line goes through (0,-2) and has a slope 1/3. What point is also on the graph of the line?

A.) (1,1)
B.) (3,-1)
C.) (-1,-5)
D.) (3,3)

Answer 1

B

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m =
`(1)/(3)`

note the line goes through the y- axis at (0, - 2) ⇒ c = - 2

y =
`(1)/(3)` x - 2 ← equation of line

To determine which point also lies on the line, substitute the x- coordinate of the point into the equation and if the value obtained agrees with the y- coordinate of the point then it lies on the line.

(1, 1) : y =
`(1)/(3)` - 2 = -
`(5)/(3)` ≠ 1

(1, 1) does not lie on the line

(3, - 1) : y = 1 - 2 = - 1 → (3, - 1) lies on the line

(- 1, - 5) : y = -
`(1)/(3)` - 2 = -
`(7)/(3)` ≠ - 5

(- 1, - 5) does not lie on the line

(3, 3) : y =1 - 2 = - 1 ≠ 3

(3, 3) does not lie on the line

Answer 2

ans: B.) (3,-1)

Because trying the choices, it is the only choice which gives the slope of 1/3:

`(y2 - y1)/(x2 - x1) = ( - 1 - ( - 2))/(3 - 0) = ( - 1 + 2)/(3 - 0) = (1)/(3)`