Equation of a Line

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3/25 Equation of a Line

Read the following SAT test question and then select your answer.

Remember to follow the Knowsys Method and note the bottom line, assess your options, attack the problem, and loop back to check the question before you select your answer.

A line segment containing the points (0,0) and (12,8) will also contain the point

The bottom line here is which answer choice lies on the given line.

There are multiple ways to solve this problem. You could find the equation of the line, or, since the line goes through the origin, you could use ratios to find a point that has the same relationship between its x and y coordinates.

First, reduce the coordinates to lowest terms. You can arrange them in a ratio format if you wish; whether you prefer $\frac{x}{y}$ or $\frac{y}{x}$ does not matter. You might use $\frac{y}{x}=\frac{8}{12}$ since "rise over run" is also the formula for slope. Reduce this to its lowest terms and then check the answer choices for multiples.

$\frac{y}{x}=\frac{8}{12}=\frac{2}{3}$

Now convert it back to (x,y) format. Make sure the x and y go in the right places.

(3,2)

A) (2,3)

B) (2,4)

C) (3,2)

D) (3,4)

E) (4,2)

The answer is C.

On sat.collegeboard.org, 58% of responses were correct.

For more help with math, visit www.myknowsys.com!