Slope-Intercept Form and Perpendicular Lines

Which of the following has a y-intercept of 3 and is perpendicular to the line 4x - 2y = 6?
A.)  2y + 3x = -3
B.)  y + 3x = 2
C.)  2y - x = 6
D.)  y - 2x = 4
E.)  2y + x = 6

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Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

Also, perpendicular lines have slopes which are negative reciprocals of each other.

Get the given line into slope-intercept form, so that the slope can be identified.

4x - 2y = 6   {given line}
-2y = -4x + 6   {subtracted 4x from each side}
y = 2x - 3   {divided each side by -2}

slope of given line is 2
perpendicular slope is -1/2

The line with a slope of -1/2 and a y-intercept of 3 is the correct choice.

Get line C.)  2y - x = 6 into slope-intercept form
2y = x + 6   {added x to each side}
y = (1/2)x + 3   {divided each side by 2}
slope is 1/2 and y-intercept is 3
Line C.) 2y - x = 6 is close, but not quite

Get line E.)  2y + x = 6 into slope-intercept form
2y = -x + 6   {subtracted x from each side}
y = (-1/2)x + 3   {divided each side by 2}
slope is -1/2 and y-intercept is 3

Line E.)  2y - x = 6 is the correct choice

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