Algebra: Chapter 5, Lesson 2, page 209.
More with Exponents!
Exponents and More with Exponents
Remember, an exponent tells how many times we use a base as a factor. For example, `a^3=a⋅a⋅a`. An expression written with exponents is written using exponential notation.
For like bases, we have:
- Rule: `a^0=1`
- Rule: to multiply we do `a^m⋅a^n=a^(m+n)
- Rule: to divide, we do `a^m/a^n=a^(m-n)`
- Rule: for negative exponent, we can express them as positive by, `a^(-m)=1/a^m
- Rule: for raising a power to another power, `(a^m)^n=a^(mn)`
- Rule: for raising a product to a power, `(ab)^n=a^n⋅b^n`
- Rule: for raising a quotient to a power, `(a/b)^n=a^n/b^n`
Remember and MEMORIZE THESE RULES for Lessons 1 and 2. Practice here!
They are also included in the Algebra Cheat Sheet that was passed today. As long as you remember these 7 formulae, you’ll be OK. Remember, if you forget the rules, just write out the problem and see what can be simplified!
PurpleMath has an EXCELLENT 2 page tutorial, click here!
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra 1a: Chapter 7, Lesson 5, page 323
Equations and Slope
An equation `y=mx+b` is called the slope-intercept equation of a line. The slope is `m` and the y-intercept is `b`. Without having to plot points, or make a T chart, we can easily determine the slope as the coefficient in front of the `x` variable and the y-intercept as `(0, b)`, the constant in the slope-intercept equation.
If the equation is not of the slope-intercept form, solve for `y` to isolate it, just like we have done in the past. The key is to have the `y` on one side of the equation and the `x` and its coefficient and the constant `b` on the other side. Usually, you have to add/subtract terms first, then multiply/divide by the coefficient in front of the `y`.
You can easily plot an equation. Start with the `(0, b)` y-intercept and then use the slope definition of `m=(rise)/(run)` to move up/down and then left/right on the graph paper as determined by the values of the rise and run. Remember to watch the signs of the rise and run.
For example, find the slope of:
`2x + 3y = 7`
first subtract `2x` from both sides
`2x – 2x + 3y = -2x +7`
to give us
`3y = -2x + 7`
divide both sides by `3` to isolate the `y`
`y = (-2/3)x + 7/3`
and the slope is then `(-2/3)` and the y-intercept is `(0, 7/3)`
See these examples from purplemath.com too! Here are others to help you graph equations given the slope m and the y-intercept b.
Two of tonight’s homework problems solved by MrE are here! Just click it!