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Thepotemich [5.8K]
3 years ago
12

Write the equation of a line that is perpendicular to the given line and that passes through the given point. 2x + 4y = –6; (2,

5)
Mathematics
1 answer:
Anna [14]3 years ago
7 0

First we have to find the slope of the given line. We do that by puttiing the equation into slope-interept form. or solving it for y (same thing). 2x + 4y = -6. We move the 2x over by subtraction to get 4y = -2x - 6. Divide both sides by 4 to get the slope-intercept form we are seeking. y=-\frac{1}{2}x-\frac{3}{2}. The slope that is perpendicular to that slope of -1/2 is the opposite reciprocal. Therefore, the perpendicular slope is a positive 2/1 or just 2. If this new line goes through the point (2, 5), it goes through the x value of 2 and the y value of 5. We will use those values along with the slope of 2 to solve for b in our slope-intercept equation. That looks like this: 5=2(2)+b and b = 1. That means our new equation, the one that is perpendicular to the given line, has an equation of y = 2x + 1.

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