Algebra: Chapter 7-3, p 313
Linear Equations and their Graphs
Linear equation have to have variables with a power of 1, no mixed variable products and no variables in an equation in the denominator. The easiest way to plot or graph an equation is to use the x-intercept and y-intercept.
- The x-intercept of a line is the x-coordinate of the point where the line intercepts the x-axis. To do this, all we have to do is set `y=0` and solve for x.
- The y-intercept of a line is the y-coordinate of the point where the line intercepts the y-axis. To do this, set `x=0` and solve for y!
The standard form of a linear equation in 2 variables is `Ax + By = C`, where A, B and C are constants.
For horizontal lines, the graph of y = b is the x-axis or a line parallel to the x-axis with y-intercept = b.
For vertical lines. the graph of x = a is the y-axis or a line parallel to the y-axis with x-intercept a.
Here is a great link from purplemath.com too!
Math 8: Chapter 5-2, p 229
Estimating Sums and Differences
Estimating and rounding numbers, decimals and fractions. When we round numbers, we look at the value of the place value to the right of the number we are rounding to. if the number is 5 or more, we round UP, and if the number is 4 or below, we round down. For example, if the the number is 5.24 and we are rounding to the nearest tenth, we look at the 4 (it is below 5) and we round the number to 5.2.
In estimating products and quotients, we choose whole numbers (usually) close to the numbers or fractions that we are using. Choose values that are close but at the same time, may be simple factors of the others. For example, `5.45 * 76.3` could be estimated as `5 * 80` or `400`. Remember, the estimate is just a good guess, it is NOT an exact answer!