Understanding the Slope-Intercept Form of a Linear Equation: Explained with Examples

Slope Intercept Form

The slope-intercept form of a linear equation is a way to represent a linear equation in the form of “y = mx + b”, where “m” represents the slope of the line and “b” represents the y-intercept

The slope-intercept form of a linear equation is a way to represent a linear equation in the form of “y = mx + b”, where “m” represents the slope of the line and “b” represents the y-intercept.

To understand this form better, let’s break it down:

“y” is the dependent variable or the output. It represents the values we are interested in plotting on the y-axis.

“x” is the independent variable or the input. It represents the values we are interested in plotting on the x-axis.

“m” is the slope of the line. It tells us how steep the line is and the direction in which it is sloping. A positive slope indicates an upward slant, while a negative slope indicates a downward slant. The magnitude of the slope represents the rate at which the line is rising or falling.

“b” is the y-intercept of the line. It tells us the point at which the line intersects the y-axis. In other words, it is the value of “y” when “x” is equal to zero.

To convert a linear equation into slope-intercept form, we need to isolate “y” on one side of the equation. Let’s see an example:

Suppose we have the linear equation: 2x – 3y = 9

To convert it into slope-intercept form, we want to rearrange the equation to solve for “y”.

First, let’s isolate “y” by subtracting 2x from both sides:
-3y = -2x + 9

Next, let’s divide the entire equation by -3 to solve for “y”:
y = (2/3)x – 3

Now, we have our equation in the slope-intercept form “y = mx + b”.

The slope of this line is represented by the coefficient of “x”, which is 2/3. This means that for every unit increase in “x”, “y” increases by 2/3.

The y-intercept of this line is represented by the constant term, which is -3. This means that the line intersects the y-axis at the point (0, -3).

With the equation in slope-intercept form, we can easily identify the slope and y-intercept, and use them to graph the line or solve problems related to it.

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