Standard Form - GED Math

The standard form of a line is , where are integers.

We therefore need to rewrite so it looks like .

The steps to do this are below:

Standard form of an equation is

.

Rearrange the given equation to make it look like the above equation as follows:

First, we need to find the slope of the above line.

Given two points, , the slope can be calculated using the following formula:

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set and :

Since we are looking for standard form - that is, - we do the following:

or

To rewrite in standard form, we will need the equation in the form of:

Subtract on both sides.

Regroup the variables on the left, and simplify the right.

The answer is:

The given equation is in point-slope form.

The standard form is:

Distribute the right side.

Subtract on both sides.

Add 2 on both sides.

The answer is:

The standard form of a linear equation is:

Reorganize the terms.

Add on both sides.

Subtract on both sides.

Subtract four on both sides.

The answer is:

Write the slope-intercept form of a linear equation.

Substitute the point and the slope.

Solve for the y-intercept, and then write the equation of the line.

The equation in standard form is:

Subtract from both sides.

The answer is:

The equation in standard form of a linear equation is:

The equation in standard form of a parabolic equation is:

All of the following equations are in standard form except:

This equation is in point-slope format:

The answer is:

The standard form of a linear equation is:

Distribute the right side.

Subtract on both sides.

Add 2 on both sides.

The answer is:

The equation in standard form is defined as .

The given equation is already in standard form and does not require any change to the variables.

Do not put this equation in point-slope, or the slope-intercept form.

The answer is:

The standard form of a line is defined as:

Add on both sides.

Rearrange the terms.

The answer is:

The equation in standard form is:

Add on both sides.

Simplify both sides.

If we multiply by four on both sides, we can eliminate the fraction.

The answer is:

Step 1: Find the lowest common denominator of the fractions on the right. To find the lowest common denominator in this question, we multiply the denominators together because both denominators are both prime numbers. **In the cases where the denominators are either both composite or one prime/one composite, find the lowest common denominator by breaking down the factors of the two numbers and taking the product of the factors that are in common (sometimes you will need to add an uncommon factor).

So, lowest common denominator is .

Step 2: Multiply both sides by 15.

Step 3: Simplify:

Step 4: Standard form is given when x and y are on the same side of the equation, usually written as .

So, we need to move the over, and then we have our answer:

The -intercept of the line can be seen to be at the point five units above the origin, which is . The -intercept is at the point three units to the right of the origin, which is . From these intercepts, we can find slope by setting in the formula

The slope is

Now, we can find the slope-intercept form of the line

By setting , :

The standard form of a linear equation in two variables is

,

so in order to find the equation in this form, first, add to both sides:

We can eliminate the fraction by multiplying both sides by 3:

Distribute by multiplying:

,

the correct equation.

The equation in standard form is:

Simplify the right side by distribution.

Subtract on both sides.

The equation becomes:

Subtract 3 from both sides.

The answer is:

We will first need to write the point-slope form to set up the equation.

Substitute the slope and point.

Simplify the right side.

Add 3 on both sides.

Subtract on both sides.

The answer is:

Distribute the right side.

Subtract on both sides.

The answer is:

The standard form of a linear equation is:

Multiply by two on both sides to eliminate the fraction.

Subtract on both sides.

Subtract 6 from both sides.

The answer is:

The standard form of a line is:

First, we can write the equation in slope-intercept form:

Subtract on both sides.

The answer is: