Which line is parallel to the line 8x+2y=12?
A. On a coordinate plane, a line goes through (\u22122,\u22124) and (0,4). B. On a coordinate plane, a line goes through (\u22121,1) and (3,0). C. On a coordinate plane, a line goes through (\u22122,2) and (\u22121,\u22122). D. On a coordinate plane, a line goes through (\u22123,2) and (1,3).<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n 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.<\/p>\n\n\n\n The slope (m) of the original line is (-4). For two lines to be parallel, they must have the same slope.<\/p>\n\n\n\n Next, we will find the slopes of each of the given lines to identify which one has a slope of (-4).<\/p>\n\n\n\n The slope (m) is calculated as: Calculating the slope: Calculating the slope: Calculating the slope: The only line with a slope of (-4) is C<\/strong>, which means it is parallel to the original line (8x + 2y = 12). Therefore, the correct answer is C<\/strong>.<\/p>\n\n\n\n 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.<\/p>\n","protected":false},"excerpt":{"rendered":" Which line is parallel to the line 8x+2y=12?A. On a coordinate plane, a line goes through (\u22122,\u22124) and (0,4). B. On a coordinate plane, a line goes through (\u22121,1) and (3,0). C. On a coordinate plane, a line goes through (\u22122,2) and (\u22121,\u22122). D. On a coordinate plane, a line goes through (\u22123,2) and (1,3). 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[
8x + 2y = 12
]<\/li>\n\n\n\n
[
2y = -8x + 12
]
[
y = -4x + 6
]<\/li>\n<\/ol>\n\n\n\nA. Line through ((-2, -4)) and ((0, 4))<\/h3>\n\n\n\n
[
m = \\frac{y_2 – y_1}{x_2 – x_1} = \\frac{4 – (-4)}{0 – (-2)} = \\frac{8}{2} = 4
]<\/p>\n\n\n\nB. Line through ((-1, 1)) and ((3, 0))<\/h3>\n\n\n\n
[
m = \\frac{0 – 1}{3 – (-1)} = \\frac{-1}{4}
]<\/p>\n\n\n\nC. Line through ((-2, 2)) and ((-1, -2))<\/h3>\n\n\n\n
[
m = \\frac{-2 – 2}{-1 – (-2)} = \\frac{-4}{1} = -4
]<\/p>\n\n\n\nD. Line through ((-3, 2)) and ((1, 3))<\/h3>\n\n\n\n
[
m = \\frac{3 – 2}{1 – (-3)} = \\frac{1}{4}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n