The slope of a line is called the gradient.When working with slope, it is important to understand the basic concepts of what slope measures, and how it measures it.If you know the coordinates of any two points, you can calculate the slope of the line.

Step 1: Define slope.

A straight line's slope is a measure of how steep it is.There are many branches of mathematics that use slope.In geometry, the slope can be used to plot points on a line.The correlation between two variables is described by a slope.Slope is used by economists to show and predict rates of change.People use slope in concrete ways.Slope is used to construct roads, stairs, ramps, and roofs.

Step 2: Take a line and make it rise over run.

The vertical distance between two points is referred to as the rise.The horizontal distance between two points is referred to as the run.When you learn about the slope of a line, you will often see a formula.To go from one point to the next, you need to go up 2 along the x and y axes.

Step 3: The equation has the slope of a line in it.

The slope-Intercept form of a line's equation can be used to do this.The slope-Intercept form states that y ismx+b.The slope of the line is equal to the mdisplaystyle m.You can use this formula to find the slope by rearranging the equation of a line.The slope in the equation is 3displaystyle 3.If you turn the slope into a fraction, you can still think of it as a rise over run.A whole number can be turned into a fraction.So, 31 is the displaystyle 3.This means that the line rises vertically for every unit it runs horizontally.

Step 4: Take into account the steepness of the line.

The bigger the slope, the harder the line is.A line rests on a plane.The slope of 2 is not as steep as that of 0.5.

Step 5: A positive slope can be identified.

A positive slope is one that moves up and down.In a positive slope, as xdisplaystyle increases, y displaystyle also increases.A positive number indicates a positive slope.

Step 6: A negative slope can be identified.

A negative slope moves to the right.As xdisplaystyle increases, y displaystyle decreases.A negative slope is a fraction with a negative numerator.You can think of yourself as standing on the left side of the line to remember the difference between a positive and a negative slope.It is positive if you need to walk up the line.It is negative if you need to walk down the line.If you know the difference between positive and negative slopes, you can check your calculations are reasonable.

Step 7: Understand the line's slope.

A horizontal line is a line that runs across the plane.A horizontal line has a slope of 0.If you think of lines in terms of slope, it makes sense.The rise is zero for a horizontal line, since the y displaystyle Y value never increases or decreases.The slope of a horizontal line would be 0x.

Step 8: Understand the slope of a line.

The slope of a vertical line is not known.The slope of a negative line would be y0The displaystyle x value never increases or decreases, so the run is 0.Since you can't divide by 0, any number over 0 will always be undefined.

Step 9: The formula should be set up for the slope of the line.

The formula is slope and display style.The rise is the distance between two points on a line.The run is the horizontal distance between two points.

Step 10: There are two points on the line.

You can either use two points or choose two.If the points are close together, there will be less need to simplify the slope later.You could pick the points (4, 4) and (12, 8).

Step 11: Find the vertical distance between the points.

Count up in a straight line until you reach the height of the second point.The rise of your slope is shown here.If you start with the higher point and move to the lower point, your rise will be negative.Beginning at the point, you would count up 4 positions to point.The rise of your slope is 4: slope=4rundisplaystyle textslope.

Step 12: Find the horizontal distance between the points.

When calculating the run, begin at the same point.When you reach the second point, count across in a straight line.You can see the run of your slope.If you start with the point on the right, your run will be negative.You would count over 8 positions to point at 4.So, the run of your slope is 8.

Step 13: If it's necessary, simplify.

The slope would be simplified just as it would any fraction.The slope of 48displaystyle frac48 makes it easy to see that both 8 and 4 are equal.The line moves up to the right because it is a positive slope.

Step 14: Set up the formula for the line's slope.

This formula can be used to find the slope on a line.

Step 15: Plug the coordinates into the formula.

You will not see them plotted on a graph if you use this method.It is important to keep your coordinates in the correct positions.The starting and ending points should be subtracted from each other.If your points are (-4, 7) and (-1, 3), your formula will look like this.

Step 16: The expression can be simplified.

The values are in the numerator and denominator.If it's necessary, simplify the slope.The slope would be simplified just as it would any fraction.The slope of the line is 43.Since the slope is negative, the line is moving to the right.