Introduction to Functions: Background You’ll Need 2

  • Find the slope between two points

slope formula

Slope measures how steep a line is by comparing the vertical change (rise) to the horizontal change (run) between two points. The slope formula is:

[latex]m=\dfrac{y_2-y_1}{x_2-x_1}[/latex]

To find the slope between two points:

  1. Identify the coordinates of both points: [latex](x_1, y_1)[/latex] and [latex](x_2, y_2)[/latex]
  2. Substitute the values into the slope formula: [latex]m = \frac{y_2 - y_1}{x_2 - x_1}[/latex]
  3. Calculate the numerator: [latex]y_2 - y_1[/latex] (vertical change)
  4. Calculate the denominator: [latex]x_2 - x_1[/latex] (horizontal change)
  5. Simplify the fraction if possible

Find the slope between the points [latex](2, 3)[/latex] and [latex](6, 11)[/latex].

It doesn’t matter which point you choose as [latex](x_1, y_1)[/latex] and which as [latex](x_2, y_2)[/latex]. Just be consistent with your choice throughout the calculation. If you switch the order, you’ll get the same slope value.