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Which equation describes the line that passes through (-3, 1) and is parallel to the line described by y = 4x + 1?

A) y = 4x - 13
B) y = 4x + 13
C) y = 4x - 1
D) y = 4x + 1

User Edwyn
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1 Answer

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Final answer:

The equation that describes a line parallel to y = 4x + 1, passing through (-3, 1), is y = 4x + 13. The slope must be the same for lines to be parallel, and by substituting the point into the slope-intercept formula, we find the y-intercept to be 13.

Step-by-step explanation:

The question asks which equation describes a line that is parallel to the line given by y = 4x + 1 and passes through the point (-3, 1). To be parallel, a line must have the same slope as the line to which it is parallel. The given line has a slope of 4, so our parallel line must also have a slope of 4. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Using the point (-3,1), we substitute the coordinates into the slope-intercept equation and solve for b:

  • 1 = 4(-3) + b
  • 1 = -12 + b
  • b = 13

Therefore, the equation of the line is y = 4x + 13, which matches option B.

User Ali Yousefi
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