Point Slope Word Problems

Sometimes instead of giving a rate, a word problem gives two sets of information that can be converted into points.

Then it asks you to find the slope and write an equation. For these questions, you will use the slope formula.

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This formula looks like this.

It’s included in the GED formula sheet that you can always access during the test. To better understand how it works, let’s solve this problem. John has a weekend job. One weekend, he earns $140 by working 4 hours. Another weekend, he earns $210 by working 6 hours.

If John would graph an equation that would be representing his total of earnings based on his hours worked, what now would the slope be of that graph?

Well, if we would put both John’s earnings on a graph, we would need to convert these earnings to points, two ordered pairs. One point would be (4 and, 140) and the second (6 and 210). Now, we can use these points and plug them into our formula.

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As you see the formula asks for x and y values. These y and x values come from our ordered pairs.

We know from a previous lesson that the first number in an ordered pair is the x value and the second is the “y”-value. The x1 and y1 are the value from our first ordered pair. And the x2 and  y2 come from the second ordered pair.

So, now we can replace y and x values with numbers in our formula. 210-140/6-4. And we end up with 70/2. It’s 35, so our slope is 35.

That’s it. If John would graph the equation, the slope of a line would be 35. Now, it’s your turn. Let’s solve a few quizzes.

Last Updated on June 13, 2022.