Math as a Second Language?
- Math: Asymptote
English: An invisible barrier that you almost touch, but never do.- Math: dy/dx
English: Velocity- Math: Second Derivative
English: Acceleration
As a math tutor and representative from Mathtopia, I translate math jargon for people living with math anxiety. Information is only good when it's useful.
Algebra forces students to manipulate a function or an equation or a story into a useful problem solving tool — the almighty graph. Become your own Mathtopia Ambassador. Translate linear functions into a graph-friendly format, slope intercept form.
1. Two Formats of Linear Functions
Standard Form: ax + by = c
Examples:
- 5x + 3y = 18
- -¾x + 4y = 0
- 29 = x + y
Slope intercept form: y = mx + b
Examples:
- y = 18 - 5x
- y = x
- ¼x + 3 = y
The primary difference between these two forms is y. In slope intercept form — unlike standard form —y is isolated. If you're interested in graphing a linear function on paper or with a graphing calculator, you'll quickly learn that an isolated y contributes to a frustration-free math experience.
Slope intercept form gets straight to the point:
y = mx + b
- m represents the slope of a line
- b represents the y-intercept of a line
- x and y represent the ordered pairs throughout a line
Learn how to solve for y in linear equations with single and multiple step solving.
2. Single Step Solving
Example 1: One Step
Solve for y, when x + y = 10.
1. Subtract x from both sides of the equal sign.
- x + y - x = 10 - x
- 0 + y = 10 - x
- y = 10 - x
Note: 10 - x is not 9x. (Why? Review Combining Like Terms.)
Example 2: One Step
Write the following equation in slope intercept form:
-5x + y = 16
In other words, solve for y.
1. Add 5x to both sides of the equal sign.
- -5x + y + 5x = 16 + 5x
- 0 + y = 16 + 5x
- y = 16 + 5x
3. Multiple Step Solving
Example 3: Multiple Steps
Solve for y, when ½x + -y = 12
1. Rewrite -y as + -1y.
½x + -1y = 12
2. Subtract ½x from both sides of the equal sign.
- ½x + -1y - ½x = 12 - ½x
- 0 + -1y = 12 - ½x
- -1y = 12 - ½x
- -1y = 12 + - ½x
3. Divide everything by -1.
- -1y/-1 = 12/-1 + - ½x/-1
- y = -12 + ½x
Example 4: Multiple Steps
Solve for y when 8x + 5y = 40.
1. Subtract 8x from both sides of the equal sign.
- 8x + 5y - 8x = 40 - 8x
- 0 + 5y = 40 - 8x
- 5y = 40 - 8x
2. Rewrite -8x as + - 8x.
5y = 40 + - 8x
Hint: This is a proactive step toward correct signs. (Positive terms are positive; negative terms, negative.)
3. Divide everything by 5.
- 5y/5 = 40/5 + - 8x/5
- y = 8 + -8x/5