Question

The graph below represents which system of inequalities?
A. y < = to -2x + 3
y < = to x + 3
B. y > = to -2x + 3
y > = to x + 3
C. y < = to -3x + 2
y < = to -x + 2
D. y > -2x + 3
y > x + 3

Answer 1

From the graph, we know that the slope of each line is negative, so already we can cross out any answer that shows a positive slope.
Next, we know that the shaded area is below each function. What does this tell you about the inequality?
Hope this helps!

Answer 2

I mostly need help on how to do the equations so that i can get the answer

Answer 3

You actually don't need to know the equations of the functions. The answer to this can be found using the process of elimination and the information I gave you above. In fact, there is only one answer where the slopes of both functions are negative, so you don't even need to make the connection that the shaded area is below the functions.

Answer 4

Wouldn't I have to solve the equation to find out if it's slope is positive or negative though?

Answer 5

Not necessarily! All of the options are in slope-intercept form, y = mx + b, where m is the slope. A function that goes down from left to right has a negative slope. A function that goes up from left to right has a positive slope. Since the functions goth go down from left to right, we know that the slope will be negative.

Answer 6

So it would be C then?

Answer 7

Yes, You are correct! Glad I could help :) Let me know if you have any other questions!

Answer 8

Thank you so much! :)

Answer 9

To find the equation of a function, you can use slope-intercept form: y = mx + b, where m = slope and b = y-intercept, or where x = 0.
To solve for the slope of a function, you can use the slope formula:
\[m = \frac{ y _{1} - y _{2}}{ x _{1}- x _{2} }\]
Where there are two points on the function
\[(x _{1}, y _{1}) and (x _{2}, y _{2})\]
Does this make sense?