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Albert drew the line represented by this equation on a coordinate plane.

y= -1/2+5

On the same coordinate plane, Penny drew a line that is perpendicular to Albert's line and passes through

the point (-4,3) Which of the following equations represents Penny's line?

A. 2x+5

B. y 2r +11

C. y=-2x-5

D. y=-2r-11

User GrantJ
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1 Answer

4 votes

Final answer:

The correct equation for Penny's line, which is perpendicular to Albert's line represented by y = -1/2x + 5 and passes through the point (-4,3), is y = 2x + 11. This is found by taking the negative reciprocal of the original line's slope and using the point-slope formula.

Step-by-step explanation:

The student is asking about the equation of a line that is perpendicular to an existing line and passes through a specific point on a coordinate plane. To solve this, we must understand the concept of slope and how it affects the orientation of lines in relation to one another. The slope is a measure of how steep a line is and is represented by the m in the line equation y = mx + b, where b is the y-intercept.

Albert's line has an equation y = -1/2x + 5. Since the slope of Albert's line is -1/2, the slope of a line perpendicular to it will be the negative reciprocal, which is 2. Penny's line passes through the point (-4,3), so using the point-slope form of the line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we can find Penny's line equation.

Substitute the point (-4,3) and the slope 2 into the point-slope equation to get y - 3 = 2(x + 4). Simplifying this, we get y = 2x + 11. Therefore, the correct equation that represents Penny's line is y = 2x + 11, which means Option B is the correct choice, assuming the correct format of Option B should be y = 2x +11.

User Kazuya  Gosho
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8.4k points