Slope-Intercept Form

The slope-intercept form of a linear equation is written as:

y = mx + b

Where:

• y is the y-coordinate of a point on the line.
• x is the x-coordinate of a point on the line.
• m is the slope of the line.
• b is the y-intercept of the line, which is the point where the line crosses the y-axis.

Finding the Slope and Y-Intercept

To write an equation in slope-intercept form, you need to find the slope (m) and the y-intercept (b).

The slope (m) is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

The y-intercept (b) is the value of y when x is 0. You can find it by looking at the point where the line crosses the y-axis or by substituting x = 0 into the equation of the line and solving for y.

Example

Let's say we have two points on a line: (2, 5) and (4, 11). We can find the slope and y-intercept of the line using the formula for slope and the given points.

First, we find the slope:

m = (11 - 5) / (4 - 2) = 6 / 2 = 3

Next, we find the y-intercept. We can use the point (2, 5) and the slope-intercept form equation:

y = mx + b

5 = 3(2) + b

b = 5 - 6 = -1

So the equation of the line in slope-intercept form is:

y = 3x - 1

Study Guide

1. Understand the meaning of slope and y-intercept in the context of linear equations.
2. Practice finding the slope and y-intercept given two points on a line.
3. Learn how to use the slope-intercept form to graph a line.
4. Practice converting an equation from standard form to slope-intercept form.
5. Work on real-world problems that involve using the slope-intercept form of a linear equation.

Remember, the slope-intercept form is a powerful tool for understanding and working with linear equations, and it's important to practice applying it to different situations.

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