Slope is the angle at which a line differs from the horizontal. On a coordinate plane, slope is defined as change in y, divided by change in x, also known as rise over run.
Know MoreA straight line always has the same slope no matter how much of it considered. For convenience, find two points where the line intersects the coordinate plane at easy-to-read points rather than between whole numbers.
If you chose the points (0, 3) and (3, -3), for example, begin by finding the difference between the two y coordinates. In this case, the answer is either 6 or -6, depending on which order you perform the operation. As long as you perform the operation in the same order when you find the difference between x coordinates, this difference does not matter.
If you subtracted 3 from -3 to find the value for change in y, subtract 0 from 3 to find the change in x. If you originally subtracted -3 from 3 to find the change in y, then subtract 3 from 0 to find the change in x.
Depending on the order you chose, you are either dividing -6 by 3, or 6 by -3. In either case, the answer is -2. This is the slope of the line. In the standard form for a linear equation, y = mx + b, m stands for the slope.
The slope and the y-intercept of a line can be found graphically and mathematically. Use the slope equation and the slope intercept equation to find both variables mathematically, or view the graph of the line to determine the y-intercept and the slope.
Full Answer >There are two components to the slope of a line: its direction and its magnitude. Find the slope of a line by observing whether, from left to right, the line rises or falls and whether the line is vertical or horizontal. Then, take the coordinates of any two points on the line and divide the difference in the points' y-axis values by the difference in their x-axis values.
Full Answer >To calculate the gradient of a line, divide the change in height between the beginning and end of the line by the change in its horizontal distance. Arguably the easiest way to do this is to plot the line on a pair of axes. For example, if a line started at (0,0) and ended at (4,4), its change in height would equal 4, and the change in horizontal distance would also equal 4. Divide 4 by 4 to get 1; therefore, the gradient of the line would equal 1.
Full Answer >To find the slope of the tangent line to the graph of a function at a point, find the derivative of the function, then plug in the x-value of the point. Completing the calculation takes just a few minutes by hand, or a calculator can be used.
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