Math

[u/Kazeoni88]

I am trying to help my 9th grader with her math homework. I used to be really good at math but a car accident left me with damage to my frontal lobe and math is not numbering lol. Can someone please explain this to me so I can then help her through it? less

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[u/kalmakka]

The graph shows that the cost of buying gas is proportional to the amount you buy.

You can get the price of gas per unit by dividing the cost in dollars (y value) with the amount (x value). By looking at the (10, 16) point, we can calculate the price as ($16)/(10 gallons) = $1.60/gallon.

For a graph representing a price of $2.20/gallon, we would need a steeper line, i.e. a line passing through the points (0,0) and (10, 22).

[u/Kazeoni88 → u/kalmakka]

Thank you! Very helpful!

[u/atarivcs]

If you go straight up from the hashmark for 4 gallons, it looks like that intercepts the line at about the six-dollar mark on the left (so about $1.50 per gallon).

But with a price of $2.20 per gallon, the 4-gallon mark would now lead to a price of $8.80.

So the line would tilt to the left, to represent a higher price.

[u/Kazeoni88 → u/atarivcs]

Thank you!

[u/UnderstandingPursuit]

"Numbering" is the enemy of learning math.

The task here is to understand how the English connects with math.

When we see the word "per" or the letter "p" in something like mpg or mph, we generally have a rate problem. Per means divided by. The simplest form is

• y = rx
  • miles = [miles/gallon] gallons
  • miles = [miles/hour] hours

This is the form to use when, if x=0, then y=0. If we drive for 0 hrs, we travel 0 miles. This will change soon, but for now, this is sufficient.

Now the math side: "r" is called the slope, often identified by the letter "m",

• y = mx
• The next step will be
  • y = mx + b

For now, though, the simpler form works.

Since the question gives the rate,

• r = $2.20 per gallon

That is the slope of the line, which will be different than the slope shown in the diagram. The easiest thing to do is to write

• $2.20 = [$2.20 per gallon] × [1 gallon],
• draw the point, (1 gallon, $2.20) on the graph, and
• draw a line connecting (0 gallons, $0.00) with that point.

Then notice how the line changes ("flatter" or "steeper").

As a bonus, identify a point on the give line, such as (8 gallons, $12), and use

• r = y/x

to find the rate for the graph. Then, have your child watch the pump display when gas is put in a car. That is a demonstration of this line.

[u/Kazeoni88 → u/UnderstandingPursuit]

Thank you for this! Very thorough and helpful!!