Understanding the Slope-Intercept Form: A Guide to Linear Equations and Graphing

Slope-Intercept Form of a Line

The slope-intercept form of a line is one of the most commonly used forms to represent linear equations

The slope-intercept form of a line is one of the most commonly used forms to represent linear equations. It is written in the form y = mx + b, where m represents the slope of the line, and b represents the y-intercept.

The slope (m) of a line determines how steeply or gradually the line slants. If the slope is positive, the line rises from left to right. If the slope is negative, the line descends from left to right. A slope of 0 indicates a horizontal line.

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0. At the y-intercept, the value of x is always 0, so the equation becomes simply y = b.

To write an equation in slope-intercept form, you need to know the slope (m) and the y-intercept (b). If you have the slope and a point on the line, you can easily find the y-intercept using the point-slope form:

y – y1 = m(x – x1)

where (x1, y1) is a point on the line.

Here’s an example: Let’s say we have a line with a slope of 2 and a point (3, 5) on the line. We can use the point-slope form to find the equation:

y – 5 = 2(x – 3)

Next, we can simplify the equation:

y – 5 = 2x – 6

Finally, rearrange the equation to be in slope-intercept form:

y = 2x – 1

In this example, the slope of the line is 2, and the y-intercept is -1. Therefore, the equation of the line is y = 2x – 1, which can be graphed as a line on the coordinate plane.

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