Question

which line is parallel to the line 8x + 2y = 12?

Explanation:

Step1: Rewrite the given line in slope - intercept form

$8x + 2y=12$ becomes $y=-4x + 6$ after algebraic manipulation.

Step2: Recall the slope - parallel line relationship

Parallel lines have equal slopes. The slope of the given line is $m=-4$.

Step3: Calculate slopes of graphed lines

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for points on each graphed line. The third graph has a slope of $-4$.

Answer:

First, rewrite the given line $8x + 2y=12$ in slope - intercept form $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept).

1. Solve $8x + 2y=12$ for $y$:

• Subtract $8x$ from both sides: $2y=-8x + 12$.
• Divide each term by 2: $y=-4x+6$. The slope of the line $8x + 2y = 12$ is $m=-4$.

1. For a line to be parallel to $y=-4x + 6$, it must have the same slope $m=-4$.

• Calculate the slopes of the lines in the graphs using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line.
• For the first graph: Let's assume two points $(0,4)$ and $(- 1,-4)$. Then $m=\frac{4+4}{0 + 1}=8$.
• For the second graph: Let's assume two points $(0,2)$ and $(2,0)$. Then $m=\frac{0 - 2}{2-0}=-1$.
• For the third graph: Let's assume two points $(0,2)$ and $(1,-2)$. Then $m=\frac{-2 - 2}{1-0}=-4$.
• For the fourth graph: Let's assume two points $(0,1)$ and $(2,2)$. Then $m=\frac{2 - 1}{2-0}=\frac{1}{2}$.

The line in the third graph is parallel to the line $8x + 2y = 12$.