Which line is parallel to the line 8x+2y=12?
A. On a coordinate plane, a line goes through (−2,−4) and (0,4). B. On a coordinate plane, a line goes through (−1,1) and (3,0). C. On a coordinate plane, a line goes through (−2,2) and (−1,−2). D. On a coordinate plane, a line goes through (−3,2) and (1,3).
The Correct Answer and Explanation is :
To determine which line is parallel to the line given by the equation (8x + 2y = 12), we first need to find the slope of the original line. We can do this by rearranging the equation into slope-intercept form (y = mx + b), where (m) is the slope.
- Start with the original equation:
[
8x + 2y = 12
] - Solve for (y):
[
2y = -8x + 12
]
[
y = -4x + 6
]
The slope (m) of the original line is (-4). For two lines to be parallel, they must have the same slope.
Next, we will find the slopes of each of the given lines to identify which one has a slope of (-4).
A. Line through ((-2, -4)) and ((0, 4))
The slope (m) is calculated as:
[
m = \frac{y_2 – y_1}{x_2 – x_1} = \frac{4 – (-4)}{0 – (-2)} = \frac{8}{2} = 4
]
B. Line through ((-1, 1)) and ((3, 0))
Calculating the slope:
[
m = \frac{0 – 1}{3 – (-1)} = \frac{-1}{4}
]
C. Line through ((-2, 2)) and ((-1, -2))
Calculating the slope:
[
m = \frac{-2 – 2}{-1 – (-2)} = \frac{-4}{1} = -4
]
D. Line through ((-3, 2)) and ((1, 3))
Calculating the slope:
[
m = \frac{3 – 2}{1 – (-3)} = \frac{1}{4}
]
Conclusion
The only line with a slope of (-4) is C, which means it is parallel to the original line (8x + 2y = 12). Therefore, the correct answer is C.
In summary, the determination of parallel lines revolves around their slopes. Since parallel lines share the same slope, identifying the slope of the given lines helped us find that line C, with a slope of (-4), is parallel to the original line.