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Which of the following lines is perpendicular to the line x + 4y = 24 and passes through the point (5,-2)?

a) 4x + y = 3
b) 2x - 8y = 16
c) 3x + 4y = 7
d) 6x - 2y = 14

1 Answer

3 votes

Final answer:

To find the line perpendicular to x + 4y = 24 and passing through the point (5,-2), we need to determine the slope of the given line and find its negative reciprocal. Then we can use the point-slope form of an equation to find the y-intercept.

Step-by-step explanation:

To find the line that is perpendicular to the line x + 4y = 24 and passes through the point (5,-2), we need to determine the slope of the given line and find its negative reciprocal.

The slope of the given line can be found by rearranging the equation in the form y = mx + b, where m is the slope. The equation becomes y = (-1/4)x + 6. Therefore, the slope is -1/4.

The negative reciprocal of -1/4 is 4/1, which means the perpendicular line will have a slope of 4.

Now, we can plug the point (5,-2) and the new slope into the equation y = mx + b to find the y-intercept, b. The equation becomes -2 = 4(5) + b, which simplifies to -2 = 20 + b. Solving for b, we get b = -22.

Thus, the equation of the line perpendicular to x + 4y = 24 and passing through the point (5,-2) is 4x - y = -22.

User Sandris
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