Functions Worksheets

Practice and master functions with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

Standard form of a line

By Adhiti Rajesh

Learn what the standard form of a line is and how to use it in math problems. Understand the standard form of a line, example problems and practice problems at Thinkster Math.

Why is this concept useful?

This equation allows us to understand the x and y intercepts of a line quickly.

Where does this concept fit into the curriculum?

High School

What is the Standard form of a line? It is a way to write the equation of a line that is defined by Ax + By = C, where A,B, and C are real numbers and A and B are not zero.


How to use the Standard Form of a Line:

We can use the standard form of a line to quickly understand the x and y intercepts of the line.

For example, the line 2x + 3y = 12

If we set x=0, then 3y = 12 and y = 4. So the y intercept is (0,4)

If we set y=0, then 2x = 12 and x = 6. So the x intercept is (6,0)

We can also convert the slope-intercept form of a line into the standard form.

For example y= 3/8(x) + 5

First, put all variables on one side:

y – 3/8(x) = 5

Then, multiply the entire equation by the denominator

8y – 3x = 40 or -3x +8y = 40

Sample Math Problems

Question

What is the x intercept of 5x + 3y = 15

Solution

To find the x intercept, set y=0.

When y=0, 5x=15 and x = 3. Therefore, the x intercept is (3,0)

Question

What is the y intercept of 5x + 3y = 15

Solution

To find the y intercept, set x=0.

When x=0, 3y = 15 and y = 5. Therefore, the x intercept is (0,5)

Question

What is y = -2x + 2/7 in standard form?

Solution

y + 2x = 2/7

7 (y + 2x = 2/7)

7y + 14x = 2 or 14x + 7y = 2

Question

What is y = 2/3(x) + 5 in standard form?

Solution

y – 2/3x = 5

3(y – 2/3x = 5)

3y – 2x = 15

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Practice Math Problems

1) What is the x intercept of 4x + 5y = 20?

2) What is the y intercept of 4x + 5y = 20?

3) What is y = 2/3(x) – 6 in standard form?

4) What is y = -4x + 2/7 in standard form?

Related Topics

By Puja Varude

Normal Distribution

By Patricia Martin

Tossing a Coin

By Mandi Elam

Properties of Exponents

By Debi DalPezzo

Solve for x

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?

A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.

Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.

Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!

Start 7-Day Free Trial