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Math  /  Algebra

QuestionCheck here for instructional material to complete this problem. Find the approximate slope of the line that contains the points (−3.1,5.9)(-3.1,5.9) and (−2.7,2.4)(-2.7,2.4). State whether the line is increasing, decreasing, horizontal, or vertical.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is □\square (Type an integer or decimal rounded to two decimal places as needed.) B. The slope is undefined.

Studdy Solution

STEP 1

1. We are given two points: (−3.1,5.9)(-3.1, 5.9) and (−2.7,2.4)(-2.7, 2.4).
2. We need to find the slope of the line that passes through these points.
3. The slope will help determine if the line is increasing, decreasing, horizontal, or vertical.

STEP 2

1. Recall the formula for the slope of a line given two points.
2. Substitute the given points into the slope formula.
3. Calculate the slope.
4. Determine the nature of the line based on the slope.

STEP 3

Recall the formula for the slope of a line given two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Substitute the given points (−3.1,5.9)(-3.1, 5.9) and (−2.7,2.4)(-2.7, 2.4) into the slope formula:
Let (x1,y1)=(−3.1,5.9)(x_1, y_1) = (-3.1, 5.9) and (x2,y2)=(−2.7,2.4)(x_2, y_2) = (-2.7, 2.4).
m=2.4−5.9−2.7−(−3.1) m = \frac{2.4 - 5.9}{-2.7 - (-3.1)}

STEP 5

Calculate the slope:
m=2.4−5.9−2.7+3.1 m = \frac{2.4 - 5.9}{-2.7 + 3.1}
m=−3.50.4 m = \frac{-3.5}{0.4}
m=−8.75 m = -8.75

STEP 6

Determine the nature of the line based on the slope:
Since the slope m=−8.75 m = -8.75 is negative, the line is decreasing.
The correct choice is: A. The slope is −8.75-8.75.

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