Question

The graph shows a line and two similar triangles.

On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.

Which expression finds the equation of the line?
StartFraction y Over x EndFraction = three-halves
StartFraction y Over x EndFraction = two-thirds
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
StartFraction y Over 3 EndFraction = StartFraction x Over 2 EndFraction

Answer 1

B

Step-by-step explanation:

(-_-)

Answer 2

Answer: Choice B)
`(y)/(x) = (2)/(3)`

This is the same as saying y/x = 2/3

Or I suppose you could say "y over x = two-thirds".

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Step-by-step explanation:

Recall that slope is rise over run

slope = rise/run

The rise being the change in y, while the run is the change in x.

So we could informally think of it as slope = y/x

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Since we're told that it "has a rise of 2 and run of 3", this means slope = 2/3.

The slope is both y/x and also 2/3.

Equating the two expressions leads us to y/x = 2/3. This is why choice B is the final answer.

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Side notes:

• This trick only works when the line goes through the origin (0,0)
• To rephrase the last bullet point, the line must have y intercept 0.
• If you multiplied both sides by x, then you get y = (2/3)x