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Math  /  Algebra

Question10. The graph of a linear function is shown in the УФ 10 coordinate plane. What is the rate of change -10-8-6-4-2 8- 6- 4. 2 -6 -8 10 2 4 6 8 10 x in y per unit change in x for this linear function? A -5 B -2.5 C -2 D -0.4

Studdy Solution

STEP 1

1. The graph represents a linear function.
2. The line passes through the points (−10,8)(-10, 8) and (10,−8) (10, -8) .
3. The rate of change is equivalent to the slope of the line.

STEP 2

1. Identify the coordinates of the two points on the line.
2. Use the slope formula to calculate the rate of change.
3. Compare the calculated slope to the given options.

STEP 3

Identify the coordinates of the two points on the line: (−10,8)(-10, 8) and (10,−8) (10, -8) .

STEP 4

Use the slope formula to calculate the rate of change: The slope m m is given by the formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute the coordinates (x1,y1)=(−10,8)(x_1, y_1) = (-10, 8) and (x2,y2)=(10,−8)(x_2, y_2) = (10, -8) into the formula: m=−8−810−(−10)m = \frac{-8 - 8}{10 - (-10)}

STEP 5

Calculate the differences in the coordinates: m=−1620m = \frac{-16}{20}

STEP 6

Simplify the fraction: m=−45=−0.8m = \frac{-4}{5} = -0.8

STEP 7

Compare the calculated slope −0.8-0.8 to the given options: The rate of change is not listed among the options A, B, C, or D.
The calculated rate of change is:
−0.8 \boxed{-0.8}

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