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How to Go From Standard Form Equations to Slope-Intercept Form

standard form equation: man writing on the blackboard

The standard form equation is a linear equation that contains two variables, usually (but not limited) to x-terms and y-terms, that are on the same sides of the equation: Ax + By = C

Coefficients A, B, and C must be whole number integers that have no decimals or fractions. In the standard form equation, coefficients B and C can be positive or negative numbers, but coefficient A must be a positive number.

Point-Slope, Slope-Intercept, and Standard Form Equations

A linear equation is the equation of a line on a graph. Linear equations come in different forms, like point-slope form and slope-intercept form. Let’s explain each of these forms.

Standard form:

standard form equation

Writing an equation in standard form makes it easier to find the x and y-intercepts, which is where the graph crosses the x- and y-axis. All you have to do is plug in a 0 for the y to find the x-intercept or a 0 for the x to find the y-intercept.

Point-slope form:

standard form equation: point-slope form

In point-slope form, x1 and y1 are coordinates of a point on a graphed line, and m is the line's slope.

Slope-intercept form:

standard form equation: slope-intercept form

The slope-intercept form has the slope, m, and the y-intercept, b, on the right-hand side of the equation. Since this is a useful form, you’ll often be asked to convert an equation from standard form to slope-intercept form. So let’s show you how to do this.

Converting Standard Form to Slope-Intercept Form

standard form equation to slope-intercept form

Let’s convert the following standard form equation to slope-intercept form:

converting standard form equation to slope intercept form

We want to isolate the y, so let’s start by subtracting 6x from both sides:

formula to isolate the y

As you can see, you’re left with -2y on the left. Now, we must divide both sides by -2 to isolate the y:

equation to isolate the y

Once you rearrange this equation to be in the y = mx + b format, this equation is in slope-intercept form:

rearranging equation to slope intercept form

How to Convert Standard Form Equations

As we've stated, in standard form, equations coefficients A, B, and C must be whole numbers. Let's convert the below equation, which contains fractions and negative numbers, into a proper standard form equation:

proper standard form

The first step is removing the fractions from the equations. To do this, we must determine the common factors of the two denominators, -4 and 8. The least common denominator of these two numbers is 8, so let's multiple each side by this:

formula on how to remove the fractions

Now that all the coefficients in this equation are whole numbers, we need to convert -6 into a positive number. We can do this by multiplying both sides of the equation by -1:

formula on how to convert negative to positive

Learning How to Write Standard Form Equations

Standard form is one of the three different ways to write linear equations. Finding common factors to convert equations with fractions into standard form equations makes it easier to move onto more complex math concepts, like graphing linear equations.

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