Algebra: Chapter 7, Lesson 6, page 328.
Finding an Equation of a Line
There are 2 ways that we can find an equation of a line. However, we need to have at least 2 points `(x,y)` or 1 point `(x,y)` and the slope, `m` provided. If we have those things, we can find the equation by the 2 methods below, you choose the one you like:
A. Using the slope-intercept equation, `y=mx+b`
- (Don’t forget, for this to work, you have to be given the slope, `m`, and at least 1 `(x,y)` point.)
- If you have the slope, `m`, plug it in for `m` above and pick the `(x,y)` that correspond to the point given.
- In the equation then, you have the `y`, `m` and `x` known.
- All you have to do is solve for `b`, the y-intercept.
- Solve for `b`, then plug in the `b` and `m` into the slope-intercept equation.
WARNING: IF you are not given the slope, then you are given 2 points. Given the 2 points, find the slope `m` with the equation `m=(y_2−y_1)/(x_2−x_1)`, then proceed as in step 2 above.
With this method, you have to solve for b, the y-intercept.
B. Using the point-slope equation (which is a derivation of the slope definition), `(y−y_1)=m(x−x_1)`
- (Don’t forget, for this to work, you need the slope and 1 point or at least 2 points from which you can find the slope.)
- (Notice too, that there is NO LONGER a `y_2` and `x_2`, just a `y` and `x`. LEAVE IT THAT WAY!)
- If you have the slope `m`, use it. If you have 2 points, then find the slope – like the WARNING above.
- Choose 1 of the `(x, y)` points to use for `(x_1, y_1)` and plug in the values that you know (`x_1`, `y_1`, and `m`).
- Solve the equation for `y` and remember that you have to distribute on the right side!
With this method you have to you the distribution method on the right. You DO NOT find the `b` or y-intercept.
Either method works, you choose what is most comfortable for YOU!
Here is a link to both methods from purplemath.com.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 3, Lesson 1 and 2, pages 114 and 119.
The Addition and Multiplication Properties of Equality (I call these 1 STEP EQUATIONS)
You can add, subtract, multiply or divide the same number to both sides of an equation and get an equivalent equation. We call these the addition and multiplication property of equality.
If `a=b`, then `a+c=b+c` and if `a=b`, then `ac=bc`
Subtraction and division are opposites of addition and multiplication, so we have no problems there. There are lots of examples at my favorite site, Purplemath, give these a look! Remember to show ALL the STEPS and that you can do these either vertically or horizontally. DON’T TAKE SHORTCUTS!
Examples:
(Addition)
`-6 = y-8`, we add 8, the opposite of -8
`-6+8=y-8+8`, we use the addition property to add 8 to both sides of the equation and finally,
`2=y`
(and Multiplication)
`y/9=14`, we will multiply both sides by `9/1` or just `9`
`9* (y/9)=9*14`, remembering that `9/9 =1`, we have
`y=126`
Whatever you do to an equation, do the S A M E thing to B O T H sides of that equation! If its `x+7`, then subtract 7 from both sides. If its `x-6`, then add 6 to both sides. If its `5x`, then divide both sides by `5` and if its `x/3`, then multiply both sides by `3`! Always do the opposite operation in these 1 step equations.
Two of tonight’s homework problems (lesson 1) solved by MrE are here! Just click it!
Two of tonight’s homework problems (lesson 2) solved by MrE are here! Just click it!