To find a relationship that represents a function with a lesser slope than the given linear function represented in the table, we first need to determine the slope of the function from the provided points.
From the points in the table:
- (-2, 11)
- (2, -5)
- (6, -11)
- (10, -17)
We can calculate the slope (m) between any two points using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's calculate the slope between the first two points, (-2, 11) and (2, -5):
\[ m = \frac{-5 - 11}{2 - (-2)} = \frac{-16}{4} = -4 \]
Now that we know the slope of the given function is -4, we need to check the slopes of the options provided to find one with a lesser slope (i.e., a slope that is greater than -4):
A. \( y = \frac{5}{4}x + 1 \)
Slope = \( \frac{5}{4} \) (greater than -4)
B. The function is not specified in your prompt, so we cannot assess its slope.
C. \( y = -3x + 4 \)
Slope = -3 (greater than -4)
D. The function is not specified in your prompt, so we cannot assess its slope.
From the options provided:
- Option A has a slope of \( \frac{5}{4} \) (greater than -4)
- Option C has a slope of -3 (greater than -4)
To find a lesser slope than -4, we compare -3 and -4. Since -3 is greater than -4, it is acceptable as having a lesser slope.
Thus, the function that represents a slope less than the one in the table (-4) is option C \( (y = -3x + 4) \).
3 answers