Wednesday, February 08, 2023

Linear Functions – What You Need to Know

Linear functions is one of the most frequently tested subtopics on the SAT/ACT, and students continually employ these basic functions as they progress through more and more rigorous math courses. Indeed, there’s nothing more important to master in high school mathematics than linear models and methods.

But which ideas should students fluently understand and keep in mind to score well on the SAT/ACT?

Here’s the list.

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Definition
Linear Functions: functions involving two first-degree variables (typically y^1 and x^1).

Vertical line equations
x = #. 
For example: x = 4 graphs as a vertical line through 4 on the x axis.

Horizontal line equations
y = #. 
For example: y = -4/5 graphs as a horizontal line through -4/5 on the y axis.

Oblique lines

Linear equation standard form: Ax+By = C, slope = -A/B. 
For example: 3x – 4y = 12, slope = -(3/-4) = 3/4.

Slope-intercept form: y = mx + b, slope = m = "rise/run," y-intercept = b. 
For example: y = -x, slope = -1 = -1/1, y-intercept = 0.

Parallel Lines
m1 = m2 (equal slopes).

Perpendicular Lines
m1 * m2 = -1 (opposite reciprocal slopes).

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For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this important material.

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