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What is the equation of the line that passes through 1 2 and is parallel to the line whose equation is 4x plus y - 1 equals 0?
Parallel lines have the same slope. So if you put the equation 4x + y -1 = 0 into the slope-intercept form of the equation of a line (y = mx + b), you can read the slope, m, from it. Rearranging that equation gives: y = -4x + 1. The slope of both lines is -4. If the new line passes through the (x, y) point (1, 2), you can use the point-slope form of the equation of a line and plug in the values to find the equation of the new line:
y - y1 = m(x - x1)
y - 2 = -4(x - 1)
y - 2 = -4x + 4
y = -4x + 6
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