Algebra: Chapter 7-5, p 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, 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.
See these examples from purplemath.com too! Here are others to help you graph equations give the slope m and the y-intercept b
Math 8, Chapter 5-4, p 239
Adding and Subtracting Like Fractions
To add or subtract like fractions, that is, those with the same denominator, all we have to do is keep the same denominator and add or subtract the numerators. In equation terms, `a/c + b/c = (a+b)/c` Try it out!
Here are some examples to follow.