Answer:
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.
