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Finding the Slope of a Line from a Graph - Problem 1

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To find the slope of a line given the graph of the line, you can use the slope formula. Find two points on the line and plug them into the slope formula -- change in y over change in x. Another method you can use to the slope triangle. Draw a triangle using the two points on the line by using the segment between the two points as the hypotenuse and drawing a vertical and horizontal line from one point to the other as the legs of the triangle. The legs of the triangle will help you count the vertical change (numerator of the slope) and vertical change (denominator of the slope). The direction of the line -- whether it is upward sloping or downward sloping -- will indicate whether or not the slope is positive (upward sloping) or negative (downward sloping).

Sometimes you're given a graph and you're asked to find the slope of the line, there's a couple of different ways to approach it. A lot of you guys will know this formula where slope is equal to change in y on top of the change in x and if you have two points like this, this formula is really easy. In case you haven't learned this yet, I'm going to show you another way that doesn't involve any formulas, just some good counting and the way I'm going to show you is using what's called a slope triangle.

I know two points that this line goes through, I'm going to draw the triangle that they define, here is what I mean, there it is right there, that's what I'm going to call a slope triangle and that will help me to count the vertical change and the horizontal change.

Here is what I mean, the vertical change is how much there is a difference going up and down, so I have 1, 2, 3, 4, five boxes, the horizontal change is how much change happens side to side, I'll call that 2, so my slope number is going to be something using the numbers 5 and 2, remember that slope is written as change in y on top of change in x, so my change in y was 5, my change in x is 2.

One last thing to be really carefully with though is remembering the positive or negative direction. Since this line is decreasing, and you could think of it as since I counted down 5, I'm going to make that a negative slope, like that, the slope of this line is -5/2.

One last way I could have drawn this triangle, is I might have drawn it instead of below the line, I could have drawn the slope triangle above the line and here is what that would look like; if I erase this, and instead of drawing it below the line, maybe I saw the triangle as being above the line like this, and I went through and again I just counted the horizontal change, and the vertical change, you'll see I still get -5 for my vertical change and +2 for my horizontal change, my slope is still the same thing.

So this is a handy way to find the slope of a line if you know two points and you have a graph, and you don't want to use that formulae where it has the y2 minus y1 over x2 minus x1.

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