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Lesson 9: 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:

a x + b y = c

Usually in this form,

a

b

, and

c

are all integers.

Want to learn more about standard form? Check out this video.

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

2 x + 3 y = 12

. If we set

x = 0

, we get the equation

3 y = 12

, and we can quickly tell that

y = 4

, which means the

y

-intercept is

(0, 4)

In a similar way, we can set

y = 0

to get

2 x = 12

and find that the

x

-intercept is

(6, 0)

. Now we can graph the line:

Problem 1

What is the $x$ ‍-intercept of the line $5 x - 2 y = 10$ ‍?

(

, 0)

What is the $y$ ‍-intercept of the line?

(0,

)

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

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 = \frac{3}{8} x + 5

to standard form:

\begin{aligned} y & = \frac{3}{8} x + 5 \\ - \frac{3}{8} x + y & = 5 Put all variables on one side \\ - 3 x + 8 y & = 40 Multiply by denominator \end{aligned}

Problem 1

What is $y = - 2 x - \frac{2}{7}$ ‍ in standard form?

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

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