Result

Calculation Steps

Visual Representation

About Slope and Y-Intercept

What are Slope and Y-Intercept?

The slope and y-intercept are key components of a linear equation, which describes a straight line on a coordinate plane. The slope indicates the steepness and direction of the line, while the y-intercept is the point where the line crosses the y-axis.

Formulas

The key formulas for calculating slope and y-intercept are:

1. Slope: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
2. Y-intercept: \(b = y - mx\)
3. Linear equation: \(y = mx + b\)

Where:

• \(m\) is the slope
• \(b\) is the y-intercept
• \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line

Calculation Steps

1. Calculate the slope using the slope formula
2. Use either point and the calculated slope to find the y-intercept
3. Form the equation of the line using the slope-intercept form

Example

Let's find the slope and y-intercept for a line passing through the points (1, 2) and (4, 8):

1. Calculate slope: \(m = \frac{8 - 2}{4 - 1} = \frac{6}{3} = 2\)
2. Find y-intercept: \(2 = 2(1) + b\), so \(b = 0\)
3. Equation of the line: \(y = 2x + 0\) or simply \(y = 2x\)