Learning Outcomes
Show Now we’ll look at some graphs on a coordinate grid to find their slopes. The method will be very similar to what we just modeled on our geoboards. Doing the Manipulative Mathematics activity "Slope of Lines
Between Two Points" will help you develop a better understanding of how to find the slope of a line from its graph. example Find the slope of the
line shown: Locate two points on the graph, choosing points whose coordinates are integers. We will use (0,−3)\left(0,-3\right) and (5,1)\left(5,1\right) . (0,−3)\left(0,-3\right) , sketch a right triangle, going from the first point to the second point, (5,1)\left(5,1\right) .
Notice that the slope is positive since the line slants upward from left to right. try itFind the slope from a graph
example Find the slope of the line shown: Show Solution Notice that the slope is negative since the line slants downward from left to right. (−3,7)\left(-3,7\right) and (6,1)\left(6,1\right) . (−3,7 )\left(-3,7\right) , sketch a right triangle to (6,1)\left(6,1\right) .
It does not matter which points you use—the slope of the line is always the same. The slope of a line is constant! try itThe lines in the previous examples had yy -intercepts with integer values, so it was convenient to use the y-intercept as one of the points we used to find the slope. In the next example, the yy -intercept is a fraction. The calculations are easier if we use two points with integer coordinates. example Find the slope of the line shown: Show Solution try itFinding the Slope of Horizontal and Vertical LinesDo you remember what was special about horizontal and vertical lines? Their equations had just one variable.
So how do we find the slope of the horizontal line y=4?y=4? One approach would be to graph the horizontal line, find two points on it, and count the rise and the run. Let’s see what happens. We’ll use the two points (0,4)\left(0,4\right) and (3 ,4)\left(3,4\right) to count the rise and run.
The slope of the horizontal line y=4y=4 is 00 . 00 . When the yy -coordinates are the same, the rise is 00 . Slope of a Horizontal LineThe slope of a horizontal line, y=by=b , is 00 . Now we’ll consider a vertical line, such as the line x=3x=3 , shown below. We’ll use the two points (3,0)\left(3,0\right) and (3,2) \left(3,2\right) to count the rise and run.
But we can’t divide by 00 . Division by 00 is undefined. So we say that the slope of the vertical line x=3x=3 is undefined. The slope of all vertical lines is undefined, because the run is 00 . Slope of a Vertical LineThe slope of a vertical line, x=ax=a , is undefined. example Find the slope of each line: x=8x=8 2. y=−5y=-5 Solution x= 8x=8 This is a vertical line, so its slope is undefined. y=−5y=-5 This is a horizontal line, so its slope is 00 . try itQuick Guide to the Slopes of LinesLicenses and AttributionsCC licensed content, Specific attribution
How do you find slope on a graph?Using the Slope Equation
Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
What is the formula to find the slope?Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.
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