# Welcome to Algebra I: Calculating the Slope When Given Two Points

15 minutes

Hey, guys. Welcome to Algebra 1. Today's lesson is going to focus on calculating slope when you're given two points on a line. Your knowledge of the coordinate plane and what you learned in pre-algebra will help you get through this lesson. You ready to get started? Let's go. Okay. Slope, you probably learned in algebra or pre-algebra, is a rate of change; it describes a rate. Often we'll have points in a table. You can interpret the slope or a rate that way. That's how we'll start out, to get your mind warmed up for dealing with slope. "Melissa is training for a marathon. The table below shows a record of her best times." We see, in 15 minutes, she ran 3 miles; 30, she ran 6 miles; 45, she ran 9 miles, okay? So slope or the rate of change-- let's say we wanted to see if it was positive or negative. Is Melissa getting better or not as she's training? Let's see if her distance increases as her time increases. At 15 minutes, she ran 3 miles. When the minutes increase to 30, her miles increase to 6. When the minutes increase to 45, her miles increase to 9. Okay, all right. It looks as though she is increasing. Her rate of change, or in her training, her slope, it's getting better every time. Let's look at this graphically and see what this looks like.

(female announcer) What is the slope? The graph has two plot points.

The first is at (negative 3, 1).

The other is at (negative 2, negative 1). Okay, let's see how you did. If you started from that left point, that far left point, we're going to go down one, two. Over one, two, three, four, five. If slope is rise over run, in this case is was a fall, so negative 2 over 5. That would be your slope for this problem, all right? Let's keep going. There's another way that you can determine the slope given two points; let's use this example. "What is the slope of the line "that contains these given points?

(female narrator) Use the slope formula to find the slope of the line that contains the given points.

Number 1: The points are (negative 1, 2) and (1, 10). Number 2: The points are (7, 3) and (7, 9). All right, let's see how you did. For the first one, the slope of that line that contains those two points... was 4, or maybe you wrote 4 over 1. For number two, the slope of the line that contains those two points is undefined. Okay? All right. Let's look at these to show you the work for these. Let me write the slope formula. Let's get the pen back. So M equals Y2 minus Y1 over X2 minus X1. And I'm going to label my points. So X1, Y1; X2, Y2. Now I'm just going to substitute into the formula. So Y2 minus Y1, that'd be 10 minus 2... over X2 minus X1, so that's 1 minus negative 1. So 10 minus 2, that's 8. 1 minus negative 1, that's going to become a plus. So in other words, 1 plus 1, that's 2. Then, 8 divided by 2 is 4. So the slope of that line is 4. Or visually, that would be a line... that went up, that would rise from left to right. That second one, that one that was undefined. Let's write our slope formula. So Y2 minus Y1 over X2 minus X1. Let's label our points, so X1, Y1; X2, Y2. Now, let's substitute into the slope formula. So Y2 minus Y1, that'd be 9 minus 3 over X2 minus X1, so that'd be 7 minus 7. So 9 minus 3, that's 6. 7 minus 7 is 0. It's not possible to divide any number by 0. If you put 6 divided by 0 in the calculator, you'd probably get an error saying "undefined" or "no domain." That's how I know that this slope is undefined. Don't leave the answer as 6 over 0. Write the answer as "undefined." Remember, the slope of a line that's undefined, or a line with an undefined slope, it's a vertical line, straight up and down. Okay? All right. Great job solving problems involving calculating the slope of a line by counting the rise over run on the graph or using the slope formula. Hope to see you soon for more Algebra 1. Bye!

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In this program, students will learn about calculating slope when given two points. Students also increase their understanding of the equation y=mx+b. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 15 minutes