Question

What is the standard form equation of the line shown below?

Answer 1

The answer to your question is A.

Answer 2

Answer: Choice A

x+3y = 14

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Explanation:

The general template for standard form is Ax+By = C, where A,B,C are integers.

This immediately rules out choices C and D, since they don't fit the format mentioned.

To see which of A or B we can eliminate or confirm, plug (x,y) coordinates from the graph into each answer choice. The ultimate goal is to get a true statement.

For example, the graph shows that (x,y) = (2,4) is on the line. Plug this into choice A to get...

x+3y = 14

2+3(4) = 14

2+12 = 14

14 = 14 this is true

So far so good. The point (2,4) is on the line x+3y = 14. Repeat those steps for (-1, 5) and you should get another true result. So that would confirm choice A is the answer. You only need a minimum of two points to define a unique line, meaning we only need to verify two points on the line. Anything more is just extra busy work.

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If we tried (2,4) with choice B, then,

5x+3y = 14

5(2)+3(4) = 14

10+12 = 14

22 = 14 which is false

This indicates (2,4) is not on the line 5x+3y = 14. We can rule out choice B because of this.