1. ## Linear equation question

In the Standard form any Linear equation, y = ax + b, one of our exercises is to take a real world situation and plug in the numbers and solve for the root, or zero.

My question is this. Is there a general rule, or guideline for explaining which of your known numbers into it's proper place in this equation?

I know that "a" represents the change in the output, or the "y" variable

I'm a little foggy on the others...

Any help would be greatly appreciated!!

2. Originally Posted by Mklangelo
In the Standard form any Linear equation, y = ax + b, one of our exercises is to take a real world situation and plug in the numbers and solve for the root, or zero.

My question is this. Is there a general rule, or guideline for explaining which of your known numbers into it's proper place in this equation?

I know that "a" represents the change in the output, or the "y" variable

I'm a little foggy on the others...

Any help would be greatly appreciated!!
in y = ax + b

y is the output

x is the input

a is the rate of change of the output (with respect to the input). that is, how y changes as we change x

b is the y-intercept, which is basically the intial output if no (zero) input is given

3. I'll add a somewhat different "dictionary" to Jhevon's answer. The a term is often known as the "linear coefficient" (in this case it can also be called the "leading coefficient.") The b term can be called the "constant coefficient" or constant term.

-Dan

4. Thanks for that information.

I'll use a problem we have worked on. It's all clear to me when it's explained as far as the formula goes, but I'm just a bit foggy on when your given a real world situation and knowing what numbers will represent the various parts of the formula.

For instance if I want to hire an electrician and he charges 50.00/hour with a 35.00 trip charge. He charges the trip charge regardless of whether or not he works as all.

So which parts of the equation would these numbers represent?

y is 50?

x is the number of hours?

5. Originally Posted by Mklangelo
Thanks for that information.

I'll use a problem we have worked on. It's all clear to me when it's explained as far as the formula goes, but I'm just a bit foggy on when your given a real world situation and knowing what numbers will represent the various parts of the formula.

For instance if I want to hire an electrician and he charges 50.00/hour with a 35.00 trip charge. He charges the trip charge regardless of whether or not he works as all.

So which parts of the equation would these numbers represent?

y is 50?

x is the number of hours?
if we have y = ax + b, where y = total charge, and x = number of hours, we have for this question, a = 50, and b = 35 (do you see why?)

so we have y = 50x + 35

when y = 50, we have:

50 = 50x + 35

and we simply solve for x to find the number of hours

6. $y = 50x + 35$ I wanted to put the $50x$ over 60, but i realised he charges per hour, not minute.

Heck, look at this graph, that guy sure pockets a lotta money!

You can't see it too clearly, but the graph starts at 35 on the y-axis? Do you realise why?

7. So in this case, b is the y intercept or the initial output since that is where you will start. He gets his trip charge regardless. If he had not charged for the trip, the y intercept would have been (0,0).

8. Originally Posted by Mklangelo
So in this case, b is the y intercept or the initial output since that is where you will start. He gets his trip charge regardless. If he had not charged for the trip, the y intercept would have been (0,0).
correct. since he charges for the trip, when we have zero hours of work, we still pay $35, so when x = 0, y = 35, hence we have the point (0, 35) which is the y-intercept. in addition, he charges$50 per hour, so for x hours, he charges \$50x, hence we have the 50x. y, the total charge, is the sum of these, thus, finally, we have y = 50x + 35, which is the line janvdl graphed for us

9. Thank you for your time on this!

By the way, this electrician is cheap...