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?

Answer 1

ans: B.) (3,-1)

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

$\frac{y2 - y1}{x2 - x1} = \frac{ - 1 - ( - 2)}{3 - 0} = \frac{ - 1 + 2}{3 - 0} = \frac{1}{3}$

Answer 2

Answer:

B

Step-by-step 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 = $\frac{1}{3}$

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

y = $\frac{1}{3}$ 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 = $\frac{1}{3}$ - 2 = - $\frac{5}{3}$ ≠ 1

(1, 1) does not lie on the line

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

(- 1, - 5) : y = - $\frac{1}{3}$ - 2 = - $\frac{7}{3}$ ≠ - 5

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

(3, 3) : y =1 - 2 = - 1 ≠ 3

(3, 3) does not lie on the line