Algebra: Chapter 6, Lesson 8, page 286, day #2.
Solving Equations by Factoring
The principle of zero products states that: for any rational numbers a and b, if the product `ab = 0`, then `a=0` or `b=0` or both `a` and `b = 0`.
Factor and solve equations by using the following:
- Get `0` on one side of the equation using the addition property
- FACTOR the expression on the other side of the equation
- Set each factor equal to zero
- Solve each equation.
If we have an equation with `0` on one side and a factorization on the other side, we can solve the equation by finding the values that make the factors `0`. This is even easier!
Since we are solving quadratic equations (they are NOT linear because they have an exponent that is squared, `x^2`), we can have at MOST 2 solutions. We can have NO solutions, 1 solution or 2 solutions.
Remember to use all the techniques you know to factor!
Two of tonight’s homework problems solved by MrE are here! Just click it!
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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!