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 3, page 125.
Using the Properties Together
You can solve these equations in a variety of ways. Remember the objective is to ISOLATE the variable on one side. You can add, subtract, multiply or divide the same thing on both sides of the equation.
Follow these 4 steps:
- you should solve equations with parenthesis using the distributive property
- if there are like terms on one side of the equation, collect those first.
- add and subtract the constants
- finally, multiply or divide by the coefficient (next to the variable) to isolate the variable
Practice makes perfect and be sure to SHOW ALL THE STEPS! Purplemath has some examples here about these multi-step equations.
Don’t forget to use the reciprocal, its sometimes the same as dividing but faster.
DO NOT TAKE ANY SHORTCUTS, SHOW ALL THE WORK IN ALL ITS GORY DETAIL, THIS WILL REALLY SAVE YOU IN THE LONG RUN BY CUTTING DOWN ON SILLY MISTAKES!!
Two of tonight’s homework problems solved by MrE are here! Just click it!