Question

The table represents the profit earned by a concession stand for each hot dog sold.
number sold
6
12
18
24
30
Profit
-36
-24
-12
0
12


Which equation represents y, the profit earned by the concession stand for x hot dogs sold?

y = x + 24
y = x – 36
y = 2x – 48
y = 6x + 12

Answer 1

Are you needing to put this into an arithmetic equation or just a "regular" line? Both represent linear functions, but the formatting is different for slope-intercept than for arithmetic

Answer 2

You did get that this is a linear function, right?

Answer 3

Oh forget that question; I see you have multiple choice answers and they are in slope-intercept form. First thing you need to determine is the slope. Can you do that from the data given?

Answer 4

I see you're not here right now, but will continue anyways, for when you come back.

Answer 5

The y values, the money earned, is increasing with the number of hot dogs sold, right? So the slope of the line will be a positive number, not a negative one. The difference in the y values is the amount that the money is increasing, or the slope of the line that represents the sale of hot dogs.

Answer 6

The slope is the rise over the run, the change in the y values over the change in the x values. We see that y is increasing at a constant rate of 12, while x is increasing at a constant rate of 6. Rise over run gives you the "fraction" \[\frac{ 12 }{ 6 }\]
which, when you divide out, gives you a slope of +2.

Answer 7

So far you have the y = 2x + ____

Answer 8

Now, remember that the y-intercept exists where x = 0. Even though you don't have an x value of 0 in your table, you can easily figure it out by following the pattern of growth in your x and y values. The value above the 6 in the x column would be 0, because, following the pattern, if 0 is above the 6 and we are adding 6 to each value to get to the next one, 0 + 6 = 6, which is the first value in the chart. So if x = 0, we need to find y. following the pattern in the same way, we have the value above the -36 being -48.

Answer 9

Do you see how that works?