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Use the following points to find the slope of a line and the perpendicular slope to that line (5,1) (2, -3).

a) Slope: -1; Perpendicular slope: 1
b) Slope: -4; Perpendicular slope: 1/4
c) Slope: 4; Perpendicular slope: -1/4
d) Slope: 1/3; Perpendicular slope: -3

User Chollida
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Final answer:

The slope of the line passing through points (5,1) and (2, -3) is 4/3, and the perpendicular slope to this line is -3/4. The provided answer choices do not correctly match these slopes.

Step-by-step explanation:

To find the slope of a line passing through two points (5,1) and (2, -3), we use the formula for slope, which is (change in y) / (change in x), or (y2-y1)/(x2-x1). In this case, the slope is (-3-1)/(2-5) = -4/-3, which simplifies to 4/3. Therefore, the slope of this line is 4/3.

Now, to find the perpendicular slope, we take the negative reciprocal of the original slope. This means we flip the fraction and change the sign. For a slope of 4/3, the negative reciprocal would be -3/4. So, the perpendicular slope to the line with slope 4/3 is -3/4.

None of the answer choices provided correctly identifies these slopes, suggesting that there may be a mistake in the question or the answer choices.

User Ssomnoremac
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