QuestionFebruary 2, 2026

Q. Use the graph to complete parts (a)-(c). a. Select any two points on the line to,calculate the slope. b. Compute the slope again this time reversing the order of the coordinates. c.What do you notice about the slopes you computed in parts (a)and (b)? d. Why do you think m=((p_(2)-r_(2)))/((p_(1)-r_(1)))=frac ((r_(2)-p_(2)))

Q. Use the graph to complete parts (a)-(c). a. Select any two points on the line to,calculate the slope. b. Compute the slope again this time reversing the order of the coordinates. c.What do you notice about the slopes you computed in parts (a)and (b)? d. Why do you think m=((p_(2)-r_(2)))/((p_(1)-r_(1)))=frac ((r_(2)-p_(2)))
Q. Use the graph to complete parts (a)-(c).
a. Select any two points on the line to,calculate the
slope.
b. Compute the slope again this time reversing the
order of the coordinates.
c.What do you notice about the slopes you
computed in parts (a)and (b)?
d. Why do you think m=((p_(2)-r_(2)))/((p_(1)-r_(1)))=frac ((r_(2)-p_(2)))

Solution
3.9(268 votes)

Answer

(a) and (b): The slope is the same regardless of the order of points. ### (c): The slopes are identical. ### (d): The formula symmetry ensures the slope remains consistent. Explanation 1. Calculate the slope using two points (Part a) Use the formula **m = \frac{y_2 - y_1}{x_2 - x_1}**. Select two points, e.g., (x_1, y_1) and (x_2, y_2), from the graph. Compute m. 2. Reverse the order of coordinates (Part b) Use the same formula **m = \frac{y_2 - y_1}{x_2 - x_1}**, but reverse the order of the points, e.g., (x_2, y_2) and (x_1, y_1). Compute m again. 3. Compare slopes (Part c) The slopes computed in parts (a) and (b) will be identical because reversing the order of subtraction does not change the ratio. 4. Explain the formula symmetry (Part d) The formula m = \frac{p_2 - r_2}{p_1 - r_1} is equivalent to m = \frac{r_2 - p_2}{r_1 - p_1} because reversing the subtraction in both numerator and denominator cancels out the negative signs, leaving the same slope.

Explanation

1. Calculate the slope using two points (Part a)<br /> Use the formula **$m = \frac{y_2 - y_1}{x_2 - x_1}$**. Select two points, e.g., $(x_1, y_1)$ and $(x_2, y_2)$, from the graph. Compute $m$.<br /><br />2. Reverse the order of coordinates (Part b)<br /> Use the same formula **$m = \frac{y_2 - y_1}{x_2 - x_1}$**, but reverse the order of the points, e.g., $(x_2, y_2)$ and $(x_1, y_1)$. Compute $m$ again.<br /><br />3. Compare slopes (Part c)<br /> The slopes computed in parts (a) and (b) will be identical because reversing the order of subtraction does not change the ratio.<br /><br />4. Explain the formula symmetry (Part d)<br /> The formula $m = \frac{p_2 - r_2}{p_1 - r_1}$ is equivalent to $m = \frac{r_2 - p_2}{r_1 - p_1}$ because reversing the subtraction in both numerator and denominator cancels out the negative signs, leaving the same slope.
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