Understanding the Slope-Intercept Form for Linear Equations and Its Applications

Slope Intercept Form

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

The slope-intercept form is a way to represent a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. In this form, “y” represents the dependent variable or the output, “x” represents the independent variable or the input, “m” represents the slope or the rate at which the line increases or decreases, and “b” represents the y-intercept or the point where the line crosses the y-axis.

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

Let’s say we have the equation 2x – 3y = 6. To convert it into slope-intercept form, we need to get “y” alone on one side of the equation. First, we subtract 2x from both sides of the equation to isolate the “y” term:

-3y = -2x + 6.

Next, we divide both sides by -3 to solve for “y”:

y = (2/3)x – 2.

Now the equation is in slope-intercept form, where the slope is 2/3 and the y-intercept is -2. This means that the line will increase by 2/3 for each unit increase in “x” and it will intersect the y-axis at the point (0, -2).

Using slope-intercept form, it becomes easier to graph the linear equation and find the relationship between the variables.

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