which point on the y - axis lies on the line that passes through point g and is parallel to line df? (-2, 0)…

Explanation:

Step 1: Calculate the slope of line DF

Assume coordinates from the graph: D(0, -2), F(2, 2).
Slope ( m = \frac{2 - (-2)}{2 - 0} = \frac{4}{2} = 2 ).

Step 2: Determine coordinates of point G

Assume G is at (-2, -6) from the graph.

Step 3: Form the equation of the line through G with slope 2

Using point-slope form: ( y - (-6) = 2(x - (-2)) ),
simplified to ( y + 6 = 2(x + 2) ).

Step 4: Find the y-intercept (x = 0)

Substitute ( x = 0 ): ( y + 6 = 2(0 + 2) ),
( y + 6 = 4 ), so ( y = -2 ).

Answer:

B. (0, -2)