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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:
ax+by=c
Usually in this form, a, b, and c are all integers.
Want to learn more about standard form? Check out this video.

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 2x+3y=12. If we set x=0, we get the equation 3y=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 2x=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 5x2y=10?
(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,0)
What is the y-intercept of the line?
(0,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

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=38x+5 to standard form:
y=38x+538x+y=5Put all variables on one side3x+8y=40Multiply by denominator
Problem 1
What is y=2x27 in standard form?
صرف 1 جواب چنو

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