Question

Pls hlp thx your the best

Answer 1

D

Step-by-step explanation:

To answer this question, we're going to have to calculate the rate of change for each of the relationships and then figure out which one is less than
`(3)/(4)`. So, let's do that!

• A. For this graph, just by looking at two points, it looks like for every change in x, there is a change in y of 2. So, this graph has a rate of change of 2.
• B. This table has a rate of change of
  `(5-0)/(8-4) =(5)/(4)`, using the change in y over change in x formula.
• C. Again, just by looking at this graph, we can find that for every change of 4 in x, there is a change of 3 in y. So, this graph has a rate of change of
  `(3)/(4)`.
• D. This is our last relationship. It has a rate of change of
  `(-22-(-17))/(10-2) =(-22+17)/(8) =(-5)/(8)`.

Which of these has a rate of change less than
`(3)/(4)`? Well, the only one that has a rate of change less than this is option D, since not only is the rate of change negative, but
`(5)/(8)` = 0.625 while
`(3)/(4)` = 0.75.

Hopefully, that's helpful. If you have further questions, let me know.

Answer 2

Answer: Choice D

=====================================================

Step-by-step explanation:

The given equation y = (3/4)x - 1 is of the form y = mx+b

• m = slope = 3/4 = 0.75
• b = y intercept = -1

For any linear equation, the rate of change is the same as the slope.

We're looking to see which linear function has a slope smaller than 0.75

---------------------

Choice A shows a graph of a straight line through the two points (0,-2) and (1,0)

To go from (0,-2) to (1,0) we do these two things in either order:

• go up 2
• go right 1

This "up 2, right 1" pattern leads to the slope = rise/run = 2/1 = 2

Graph A has a slope of 2 which is not smaller than 0.75, so we cross choice A off the list.

An alternative would be to use the slope formula (see parts B through D).

---------------------

Choice B is a table of values. Each row is a separate (x,y) point.

Let's pick the first two rows to generate the points (-4,-10) and (0,-5)

Apply the slope formula on those points.

`(x_1,y_1) = (-4,-10) \text{ and } (x_2,y_2) = (0,-5)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (-5 - (-10))/(0 - (-4))\\\\m = (-5 + 10)/(0 + 4)\\\\m = (5)/(4)\\\\m = 1.25`

The slope is 5/4 aka 1.25

1.25 is not smaller than 0.75, so we cross choice B off the list.

---------------------

Choice C is a line through (0,-2) and (4,1)

Use the slope formula again, or use the trick mentioned in part A.

I'll use the slope formula.

`(x_1,y_1) = (0,-2) \text{ and } (x_2,y_2) = (4,1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (1 - (-2))/(4 - 0)\\\\m = (1 + 2)/(4 - 0)\\\\m = (3)/(4)\\\\m = 0.75`

This is not smaller than 0.75, so we move on.

Choice D should be the answer because it's the only thing left.

---------------------

For choice D we have a table of values.

Pick two rows at random. I'll pick the first two rows to get the points (4, -7) and (6,-12)

Use the slope formula.

`(x_1,y_1) = (4,-7) \text{ and } (x_2,y_2) = (6,-12)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (-12 - (-7))/(6 - 4)\\\\m = (-12 + 7)/(6 - 4)\\\\m = -(5)/(2)\\\\m = -2.5`

This slope -2.5 is smaller than 0.75, so we have found the final answer.