Slope-Intercept Form Calculator

How to Calculate Slope-Intercept Form

The slope-intercept form is a way of expressing the equation of a straight line. It's one of the most common and useful forms of a linear equation.

Slope-Intercept Formula

The slope-intercept form of a line is:

\[ y = mx + b \]

Where:

• m is the slope of the line
• b is the y-intercept (where the line crosses the y-axis)
• x and y are the coordinates of any point on the line

Calculation Steps

1. If you have two points:
   • Calculate the slope using the slope formula: m = (y₂ - y₁) / (x₂ - x₁)
   • Use one of the points and the calculated slope in the point-slope form
   • Rearrange to get the slope-intercept form
2. If you have the slope and y-intercept:
   • Simply substitute the values into y = mx + b
3. If you have a point and the slope:
   • Use the point-slope form: y - y₁ = m(x - x₁)
   • Rearrange to get the slope-intercept form

Example Calculation

Let's find the slope-intercept form of a line passing through the points (1, 2) and (4, 8).

1. Calculate the slope: \[ m = \frac{8 - 2}{4 - 1} = \frac{6}{3} = 2 \]
2. Use the point-slope form with (1, 2): \[ y - 2 = 2(x - 1) \]
3. Expand: \[ y - 2 = 2x - 2 \]
4. Rearrange to slope-intercept form: \[ y = 2x - 2 + 2 = 2x \]

Therefore, the slope-intercept form is y = 2x, with a slope of 2 and a y-intercept of 0.

Visual Representation

A visual representation can help understand these concepts better. Here's a diagram showing the line y = 2x:

This diagram illustrates the line y = 2x, showing its slope and how it passes through the points (1, 2) and (4, 8).