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

Explanation:

Step1: Find slope of line DF

Let (D=(0, - 3)) and (F=(2,3)). Slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3-(-3)}{2 - 0}=\frac{6}{2}=3).

Step2: Use point - slope form with point G

Assume (G=(-3,-4)). The point - slope form of a line is (y - y_1=m(x - x_1)). Substituting (m = 3), (x_1=-3), (y_1=-4), we get (y+4 = 3(x + 3)).

Step3: Find y - intercept

The line intersects the (y) - axis when (x = 0). Substitute (x = 0) into (y+4 = 3(x + 3)): (y+4=3(0 + 3)), (y+4 = 9), (y=5) (There is a mistake above, let's use another way). Since parallel lines have the same slope. The slope of line (DF) is (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) and parallel to (DF) has the equation (y+4 = 3(x + 3)) in point - slope form. When (x = 0), (y+4=3(0 + 3)), (y+4=9), (y = 5) (Wrong, correct way: The slope of line (DF) is (m=\frac{3+3}{2-0}=3). The line passing through (G(-3,-4)) with slope (m = 3) has the equation (y+4=3(x + 3)). Expanding gives (y+4=3x+9), or (y=3x + 5). When (x = 0), (y=5) (Wrong again, correct: The slope of line (DF) is (m=\frac{3+3}{2-0}=3). The line passing through (G(-3,-4)) and parallel to (DF) has the equation (y+4=3(x + 3)). We can also use the fact that if two lines are parallel they have the same slope. The slope of (DF) is (m=\frac{3+3}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)) which simplifies to (y=3x + 5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y = 5) (Wrong, correct: The slope of line (DF): (m=\frac{3-(-3)}{2 - 0}=3). The line passing through (G(-3,-4)) with slope (m = 3) has the equation (y+4=3(x + 3)) or (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x + 5) gives (y=5) (Wrong, correct: The slope of line (DF) is (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y - y_G=m(x - x_G)), so (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) and parallel to (DF) has the equation (y+4 = 3(x + 3)) which simplifies to (y=3x+5). Points on the (y) - axis have (x = 0). Substituting (x = 0) into (y=3x+5) gives (y = 5) (Wrong, correct: The slope of line (DF): If (D=(0,-3)) and (F=(2,3)), (m=\frac{3+3}{2-0}=3). The line passing through (G(-3,-4)) with slope (m = 3) is (y+4=3(x + 3)), (y=3x + 5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), (y=3\times0 + 5=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y = 3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y - (-4)=3(x-(-3))), (y + 4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x + 5). For a point on the (y) - axis ((x = 0)), (y=3\times0+5 = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x+5) gives (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). A point on the (y) - axis has (x = 0). Substituting (x = 0) into (y=3x+5) gives (y = 5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x = 0), (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). For a point on the (y) - axis ((x = 0)), substituting (x = 0) into (y=3x+5) gives (y=5) (Wrong, correct: The slope of line (DF): Let (D=(0,-3)) and (F=(2,3)), (m=\frac{3-(-3)}{2-0}=3). The line passing through (G(-3,-4)) has the equation (y+4=3(x + 3)), (y=3x+5). When (x =