Slope Calculator

How to Calculate Slope and Slope-Intercept Form

Calculating slope and determining the slope-intercept form of a line are fundamental skills in algebra and geometry. These concepts are crucial for understanding linear relationships and graphing lines.

Slope Formula

The slope of a line represents its steepness and direction. It is calculated using two points on the line:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

• m is the slope
• (x₁, y₁) is the first point
• (x₂, y₂) is the second point

Slope-Intercept Form

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)

Calculation Steps

1. Calculate the slope using two points on the line
2. Determine the y-intercept using the point-slope form
3. Write the equation in slope-intercept form

Example Calculation

Let's calculate the slope and slope-intercept form for 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. Simplify 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).