Algebra: Chapter 5, Lesson 3, page 214.
Multiplying and Dividing Monomials
A monomial is an expression that is either a NUMERAL, an VARIABLE or a PRODUCT of numerals and variables with whole number exponents. If the monomial is a numeral, we call it a CONSTANT.
Using the properties we had from yesterday, we can use the associative and commutative properties to multiply or divide monomials.
For example, `(3x)(4x)=(3⋅4⋅x⋅x)=12x^2` or
`(x^5)(x^-2) =x^(5-2)=x^3`
Here are some more examples too!
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!