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## Algebra 1

### Course: Algebra 1>Unit 5

Lesson 5: Standard form

# Standard form review

Review linear standard form and how to use it to solve problems.

## What is the linear standard form?

This is the standard form of linear equations in two variables:
start color #11accd, a, end color #11accd, x, plus, start color #1fab54, b, end color #1fab54, y, equals, start color #e07d10, c, end color #e07d10
Usually in this form, start color #11accd, a, end color #11accd, start color #1fab54, b, end color #1fab54, and start color #e07d10, c, end color #e07d10 are all integers.

## Finding features and graph from standard equation

When we have a linear equation in standard form, we can find the x- and y-intercepts of the corresponding line. This also allows us to graph it.
Consider, for example, the equation start color #11accd, 2, end color #11accd, x, plus, start color #1fab54, 3, end color #1fab54, y, equals, start color #e07d10, 12, end color #e07d10. If we set x, equals, 0, we get the equation start color #1fab54, 3, end color #1fab54, y, equals, start color #e07d10, 12, end color #e07d10, and we can quickly tell that y, equals, 4, which means the y-intercept is left parenthesis, 0, comma, 4, right parenthesis.
In a similar way, we can set y, equals, 0 to get start color #11accd, 2, end color #11accd, x, equals, start color #e07d10, 12, end color #e07d10 and find that the x-intercept is left parenthesis, 6, comma, 0, right parenthesis. Now we can graph the line:
Problem 1
• Current
What is the x-intercept of the line 5, x, minus, 2, y, equals, 10?
left parenthesis
comma, 0, right parenthesis
What is the y-intercept of the line?
left parenthesis, 0, comma
right parenthesis

Want to try more problems like this? Check out this exercise.

## Converting to standard form

In some cases (for example when solving systems of equations), we might want to bring an equation written in another form to standard form.
Let's bring the equation y, equals, start fraction, 3, divided by, 8, end fraction, x, plus, 5 to standard form:
\begin{aligned} y&=\dfrac{3}{8}x+5 \\\\ -\dfrac{3}{8}x+y&=5\quad\gray{\text{Put all variables on one side}} \\\\ -3x+8y&=40\quad\gray{\text{Multiply by denominator}} \end{aligned}
Problem 1
• Current
What is y, equals, minus, 2, x, minus, start fraction, 2, divided by, 7, end fraction in standard form?