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Math  /  Algebra

Question3. Calculate slope from two points: a) (−9,6)(-9,6) and (−6,−9)(-6,-9) b) (−10,1)(-10,1) and (0,−4)(0,-4) c) (2,−2)(2,-2) and (9,3)(9,3) d) (−1,−7)(-1,-7) and (3,9)(3,9)

Studdy Solution

STEP 1

1. The slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]
2. Each pair of points represents a line segment, and we are tasked with finding the slope of each segment.

STEP 2

1. Identify the coordinates of the two points.
2. Apply the slope formula to calculate the slope for each pair of points.
3. Simplify the slope expression if necessary.

STEP 3

For each pair of points, identify the coordinates (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2).
a) Points: (−9,6)(-9, 6) and (−6,−9)(-6, -9)
b) Points: (−10,1)(-10, 1) and (0,−4)(0, -4)
c) Points: (2,−2)(2, -2) and (9,3)(9, 3)
d) Points: (−1,−7)(-1, -7) and (3,9)(3, 9)

STEP 4

Calculate the slope for each pair using the formula m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} .
a) m=−9−6−6−(−9)=−153=−5m = \frac{-9 - 6}{-6 - (-9)} = \frac{-15}{3} = -5
b) m=−4−10−(−10)=−510=−12m = \frac{-4 - 1}{0 - (-10)} = \frac{-5}{10} = -\frac{1}{2}
c) m=3−(−2)9−2=57m = \frac{3 - (-2)}{9 - 2} = \frac{5}{7}
d) m=9−(−7)3−(−1)=164=4m = \frac{9 - (-7)}{3 - (-1)} = \frac{16}{4} = 4

STEP 5

Simplify the slope expressions if necessary. The calculated slopes are already in simplest form.
a) Slope: −5-5
b) Slope: −12-\frac{1}{2}
c) Slope: 57\frac{5}{7}
d) Slope: 44

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