Algebra: Chapter 7, Lesson 8, page 338
Parallel and Perpendicular Lines
Parallel lines by definition have the same slope. So, for the equation of 2 lines, all we have to do is figure out what the slope is of them both. If they have the same slope, then they are parallel. Check too, however, to make sure that both lines have DIFFERENT y-intercepts. If they have the same slope and y-intercept, then they are the same line, one on top of the other.
Perpendicular lines are lines that intersect at 90° or are at right angles to each other. By definition, the slopes of 2 lines that are perpendicular, when multiplied together, have a resultant product of −1.
Remember, the slope-intercept formula to find the slope, `m`: `y = mx + b`
You MAY have to solve the equation lines for `y`, isolating it to see what the slope, `m`, is as well as the y-intercept, `b`.
Here is a link from purplemath too with more explanation and examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 3, Lesson 9, page 148.
Proportions
A ratio of 2 quantities is a comparison, often expressed as a fraction. An equation that states that 2 ratios are equal is called a proportion. I prefer to just criss-cross, or cross multiply proportional problems, but the book’s way is OK too.
For example,
`x/63=2/9`, I solve by criss-crossing. That becomes
`x*9=2*63` or `9x=63*2` or `9x=126`
and dividing both sides by 9 to clear the x, gives us `x=14`.
Here is a link from purplemath.com that has some more examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!