Content

• Steps
• Method 1 of 3: Determining the Slope
• Method 2 of 3: Calculating the Slope on a Plot
• Method 3 of 3: Calculate Slope Using Formula
• Tips

The slope characterizes the angle of inclination of the straight line with respect to the abscissa axis (X-axis).

Steps

Method 1 of 3: Determining the Slope

1. 1 The slope is equal to the tangent of the angle between the straight line and the positive direction of the abscissa axis. The larger the slope, the faster the function grows.
2. 2 A negative slope indicates a decreasing function, while a positive slope indicates an increasing one.
3. 3 The slope of a straight line parallel to the x-axis is always zero, and the slope of a straight line parallel to the y-axis does not exist.

Method 2 of 3: Calculating the Slope on a Plot

1. 1 On the graph, mark any two points for which you can find coordinates.
2. 2 Draw straight lines through the points, parallel to the X-axis and Y-axis.
   • The intersection points of these lines will lie above and below the graph, forming two right-angled triangles.Consider any of these triangles.
3. 3 Select the point on the right of the graph and find the distance between this point (origin) and the intersection point (end point) of lines parallel to the coordinate axes.
   • That is, you need to count the number of divisions on the Y-axis from the starting point to the ending point. For example, the number of divisions is 5.
   • Now select a point on the left of the graph and find the distance between this point (origin) and the intersection point (end point) of straight lines parallel to the coordinate axes. That is, you need to count the number of divisions on the X-axis from the starting point to the ending point. For example, the number of divisions is 7.
4. 4 The slope is equal to the ratio of the number of divisions on the Y-axis to the number of divisions on the X-axis; in our example, the slope is 5/7.
5. 5 Simplify the resulting fraction if possible.

Method 3 of 3: Calculate Slope Using Formula

1. 1 If you know the coordinates of the points ((x₁, y₁) and (x₂, y₂)) lying on the graph, then you can calculate the slope using the formula:
   
   (y₂ - y₁) / (x₂ - x₁)
   
   or
   
   (y₁ - y₂) / (x₁ - x₂)Both formulas are equivalent.
2. 2 Suppose given points with coordinates (-4, 7) and (-1, 3).
3. 3 Plug in the coordinates into the formula.
4. 4 Simplify the resulting fraction (if possible).

Tips

• If you are not familiar with why (-4) - (-1) = -3, then read this article.
• Formula: k = (y₂ - y₁)/(x₂ - x₁)
  where k Is the slope, (x₁, y₁) and (x₂, y₂) - coordinates of two points.