Question

The graph of a function is shown on the coordinate plane below. Which relationship represents a function with a leaser slope than the function graphed?

Answer 1

To compare between slopes, we first have to calculate the value of the slope of the graph given using the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

For this, we have to choose two points: (-3, 1), (-1, 3). Replacing the values we get:

`m=\frac{1_{}-3_{}}{-3_{}-(-1)_{}}=(-2)/(-3+1)=(-2)/(-2)=1`

Then, our slope is equal to 1.

Now, we have to calculate the slopes of the tables using the same formula and choosing 2 points.

• A

`m=(0-(-2))/(1-(-1))=(2)/(1+1)=(2)/(2)=1`

This option has the same slope as ours, then, it is not the answer.

• C

`m=(3-(-7))/(4-(-4))=(3+7)/(4+4)=(10)/(8)=1.25`

This is greater than our slope, then it is not the answer.

Also, option B has a greater slope as 5/2 = 2.5.

Finally, 1/4 = 0.25 is less than our slope.

Answer: D