Question

which point on the y - axis lies on the line that passes through point g and is parallel to line df? (-2,0) (0,-2) (0,4) (4,0)

Explanation:

Step1: Find the slope of line DF

Let \(D(-1,-3)\) and \(F(1,3)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So \(m_{DF}=\frac{3-(-3)}{1 - (-1)}=\frac{6}{2}=3\).

Step2: Use the point - slope form to find the equation of the new line

Let point \(G(-3,-5)\). The point - slope form is \(y - y_1=m(x - x_1)\). Substituting \(m = 3\), \(x_1=-3\), \(y_1=-5\) gives \(y+5 = 3(x + 3)\).

Step3: Simplify the equation

Expand the right - hand side: \(y+5=3x + 9\), then \(y=3x + 4\).

Step4: Find the y - intercept

The line intersects the \(y\) - axis when \(x = 0\). Substitute \(x = 0\) into \(y=3x + 4\), we get \(y=4\). So the point is \((0,4)\).

Answer:

C. \((0,4)\)