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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Contact Chris

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Call the Capitol Switchboard!

It's hard to not be cynical about politics, today. 

Citizenship, however, isn't politics. 

Rather, citizenship is responsibility we all share. Citizen participation is a requirement in a functioning democracy, a duty we can each discharge in multiple ways. One of the simplest is to call the Capitol Switchboard on a regular basis to leave messages for your congressional and senatorial representatives.

Here's the phone number: (202) 224-3121.

I recommend storing the number in your phone, so that when you have a few minutes you can make that time count by calling the Switchboard and leaving a message or two. A great time to do this is during the morning/evening commute, while waiting in line somewhere, or everyday just after breakfast (to make it a habit).

"The problem with democracy is that people get the government they deserve."

Do we Americans still deserve a strong, healthy democracy? Time will tell.

It’s easy to feel there’s nothing one can do. Which only furthers the degradation of the democracy we still have.

I invite you to do what you can. Calling the Capitol Switchboard only takes a few short minutes. Do so on a regular basis.

You and yours will know you did what you could to keep democracy alive in America, which is all that's required of any of us.

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.