# Interpret Linear Equations

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This video is for the redesigned SAT which is for you if you are taking the SAT in March 2016 and beyond.

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Heart of Algebra

Linear equation word problems
Example:
In 2017, Celeste's income tax was \$2,290. Her income tax rate was 10% for the first \$13,000 of her income and 15% for her income in excess of \$13,000. Which of the following best models x, Celeste's income in dollars in 2017?
a) (0.1 + 0.15)x - 13,000 = 2,290
b) 0.15 - (0.1)(13,000) = 2,290
c) (0.1)(13,000)(0.15x) = 2,290
d) (0.1)(13,000) + 0.15(x - 13,000) = 2,290
Interpret Linear Equations

Example:
The mean number of students per classroom, y, at Central High School can be estimated using the equation y = 0.8636x + 27.277, where x represents the number of years since 2004 and x ≤ 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

A) The estimated mean number of students per classroom in 2004
B) The estimated mean number of students per classroom in 2014
C) The estimated yearly decrease in the mean number of students per classroom
D) The estimated yearly increase in the mean number of students per classroom

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