So far you’ve considered lines that run “uphill” or “downhill.” Their slopes may be steep or gradual, but they are always positive or negative numbers. Let’s organize the information about the two points:įinding the Slopes of Horizontal and Vertical Lines You can just use the coordinates, keeping careful track of which is Point 1 and which is Point 2. You do not need the graph to find the slope. The run is −2, because you are then moving in a negative direction (left) 2 units. You can see from the graph that the rise going from Point 1 to Point 2 is 4, because you are moving 4 units in a positive direction (up). A triangle is drawn in above the line to help illustrate the rise and run. So you are going to move from Point 1 to Point 2. The point (0, 2) is indicated as Point 1, and (−2, 6) as Point 2. In the example below, you’ll see that the line has two points each indicated as an ordered pair. The run between these two points is the difference in the x-coordinates, or x 2 − x 1. The rise is the vertical distance between the two points, which is the difference between their y-coordinates. Point 1 has coordinates ( x 1, y 1) and Point 2 has coordinates ( x 2, y 2). The y value tells you where the point is vertically.Ĭonsider two points on a line-Point 1 and Point 2. The x value tells you where a point is horizontally. Every point has a set of coordinates: an x-value and a y-value, written as an ordered pair ( x, y). You can also find the slope of a straight line without its graph if you know the coordinates of any two points on that line. You’ve seen that you can find the slope of a line on a graph by measuring the rise and the run. The next example shows a line with a negative slope.įinding the Slope of a Line Given Two Points The greater the slope, the steeper the line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line. When you look at the two lines, you can see that the blue line is steeper than the red line. The slope of the blue line is 4 and the slope of the red line is. Substitute the values for the rise and run into the formula Slope =. The red line, going from point (-1, -2) to point (3, -1) has a rise of 1 unit. Substitute the values for the rise and run in the formula Slope =. Run is 1 unit to the right, so it is positive. This line has a rise of 4 units up, so it is positive. Start with the blue line, going from point (-2, 1) to point (-1, 5). Notice that both of these lines have positive slopes, so you expect your answers to be positive. It is positive as you moved up.Use the graph to find the slope of the two lines. Start from a point on the line, such as (2,1) and move vertically until in line with another point on the line, such as (6,3). Consider the graphs of the three lines shown below: By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. In math, slope is used to describe the steepness and direction of lines. The mathematical definition of slope is very similar to our everyday one. Interpret the slope of a linear equation as it applies to a real situation.Verify the slope of a linear equation given a dataset.Interpret slope in equations and graphs.Given a line, identify the slope of another line that is perpendicular to it.Given a line, identify the slope of another line that is parallel to it.Identify slopes of parallel and perpendicular lines.Recognize that vertical lines have slopes that are undefined.
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