Determine if the lines are parallel, perpendicular or neither. y = 4x + 12 and x + 4y = 32
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parallel
perpendicular
neither
To determine if the lines are parallel, perpendicular or neither, we need to analyze the slopes of both lines.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line. In the equation y = 4x + 12, the slope is 4.
To find the slope of the second line, x + 4y = 32, we need to rearrange it into slope-intercept form. First, isolate y: 4y = -x + 32, y = -1/4x + 8. The slope of this line is -1/4.
Since the slopes of the two lines are not equal to each other (4 is not equal to -1/4), the lines are not parallel.
To determine if they are perpendicular, we can multiply the slopes of the two lines. The product of the slopes is (4) * (-1/4) = -1. Since the product is -1, the lines are perpendicular to each other.
Therefore, the lines y = 4x + 12 and x + 4y = 32 are perpendicular.