A. The y-intercept of the function is 3. B. The x-intercept of the function is 5/3.
C. The slope of the function is negative.
D. The slope of the function is positive.

D. The slope of the function is positive.

Step-by-step explanation:

I think the best thing to start with is the slope. Lets figure it out using the slope formula, (y2-y1)/(x2-x1).

Using the points, (-4, -7) and (-3, -4),

(-4 - (-7)) / (-3 - (-4))

= 3 / 1

= 3

Right off the bat, you can see that C is incorrect.

Lets go through the other choices and check now.

Using our slope, lets write an equation in the slope intercept form.

y = -3x + b (derived from y=mx+b)

Now, lets plug in a point (let's say, (-4,-7)) to verify if 3 really is the y intercept.

-7 = 3(-4) + b

-7 = -12 +b

5 = b

Since 3 is not equal to 5, A is incorrect. That leaves us with choice B and D.

We know that the x-intercept is found as (0, a), meaning that this x intercept is (0, 5/3). Let's plug it into the equation!

0 = 3(5/3) + 5

0 = 5 + 5

0 = 10

Since this is obviously incorrect, our answer is D, the slope of the function is positive. Let me know if you have any other questions.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50