y=mx+b [Slope-Intercept] Word Problems

Word-problem questions are a big part of the GED test; many of them ask to calculate a slope. It means you will need to use the “y = mx + b” formula.

Keep in mind that when we are solving word problems, a slope usually refers to a rate. To understand it better, let’s check this example.

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When visiting Orlando, Maria needs to rent a taxi to get from a hotel to a restaurant.

The fee that the taxi company is charging is a flat $3.00 fee and for each mile an additional $0.75.

The question asks us to write a mathematical equation in the slope-intercept form that represents this situation.

What would be the slope of the graph? And what would be the cost for an 8-mile taxi ride?

If the taxi ride would cost you $15, what’s the number of miles that the taxi traveled?

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We’re going to start by writing a slope-intercept form of an equation: y = mx + b. Then, let’s take a look at what all four of these variables mean in word problems. “M” is used if they talk about a rate, a certain amount per month or year, or a minute.

Whenever you see the words: “per, each, every,” it’s a sign you should replace it with the “m” value. And the x typically stands for whatever the rate is referring to.

For example, a mile, a year, or a month.  “B” represents a one-time cost. “Y” right here always stands for the total amount.

Let’s repeat what we know and how it refers to our equation.
We know that rate per mile is $0.75.
As I mentioned before, in word problems, a rate is represented by “m”. The question also mentions that a flat fee is 3 dollars.

A flat fee is the same as a one-time payment. In word problems, a one-time payment is expressed as a “b” value.

Okay, we have decoded all variables, let’s compare these two equations. And we see that 0.75 is our m. And because the “m” stands for a slope, we know the answer to the first question. The slope is 0.75.

The second question asks how much would a taxi ride for 8 miles cost?

So, 8 is the number of miles, that in our equation, is represented by x.

Let’s replace x with 8 and calculate this equation. Let’s start with 0.75(8) plus 3.

0.75 × 8 = 6.

6+3 = 9.

Therefore, the answer is: a taxi ride for 8 miles will cost 9 dollars.

The last question asks: if a taxi ride costs $15, what’s the number of miles the taxi traveled? This time, they give us a total cost. We know that the total cost is represented by the “y”-value. Therefore we can replace the y with 15. The question asks us to come up with the number of miles the taxi traveled. When we look at the equation with plug-in numbers, we see that they ask about the x-value.

15=0.75x+3

So, we need to solve this equation for x. Like always, when solving equations, we need to isolate the x.

First, on the right side, we subtract 3 from 0.75x + 3. And what we do to the one side, we need to do the same to the other side. Therefore, on the left side, we subtract 3 from 15.

15-3=0.75x+3-3

12=0.75 x.

It’s getting better but the x is still being multiplied by 0.75, To cancel this multiplication, we need to apply the opposite operation. For this reason, we divide both sides by 0.75.

And now, on the right side, finally, we end up with the x. On the left side, we divide 12 by 0.75. It’s 16. So, x = 16. And this is our answer.

12/0.75=0.75 x/0.75

16=x

So if the taxi ride costs $15, our taxi traveled 16 miles. Now it’s your turn. Let’s solve a few quizzes.

As you see solving y=mx+b word problems is not that difficult and can be quite useful in the real life.

 

Last Updated on June 13, 2022.