Video: Identifying Graphs of Linear Equations in Standard Form

Which of the following graphs represents the equation 2𝑥 − 3𝑦 = 18? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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Video Transcript

Which of the following graphs represents the equation two 𝑥 minus three 𝑦 equals 18?

Two 𝑥 minus three 𝑦 equals 18 can be rewritten as three 𝑦 equals two 𝑥 minus 18. Dividing both sides of this equation by three gives us 𝑦 is equal to two-thirds 𝑥 minus six. This means that the slope or gradient of the equation two 𝑥 minus three 𝑦 equals 18 is two-thirds. And its 𝑦-intercept is negative six.

The only graph that has an intercept of negative six is graph A. The intercept of graph B is negative two. Graph C has an intercept of six. Graph D also has an intercept of six. And graph E has an intercept of negative nine.

Graph A also has a slope or gradient of two-thirds. This is the same as the slope of two 𝑥 minus three 𝑦 equals 18. Therefore, graph A represents the equation two 𝑥 minus three 𝑦 equals 18, which could also be written 𝑦 equals two-thirds 𝑥 minus six.

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