lgebra 2
Solving Basic EquationsSolving basic equations consists of isolating the sole variable from the rest of the equation.
Solving Basic EquationsSolving basic equations consists of isolating the sole variable from the rest of the equation.
| The purpose of basic equations is to solve for the variable in number form, or to get the single variable isolated from the rest of the equation. | 3x-8=28 |
| First add 8 to both sides. Because it is 3x-8 a +8 is needed to cancel it out from the side with the variable. | 3x+8-8=28+8 OR 3x=36 |
| Finally, to totally isolate the x, divide both sides of the equation by 3. This will cancel out the 3 that was currently being multiplied by x. | 3x/3 |
Solving Literal Equations
Solving literal equations consists of isolating the given variable from the rest of the variables.
| First, the equation and the variable that needs to be solved for is given. | Solve for "r" l=Prt |
| The rest of the steps are as if it were a basic equation. In order for r to be isolated it needs to be divided by P, so divide both sides by P. | l/P=Prt/P OR l/P=rt |
| Then t is divided from both sides. "r" is isolated and the eqution is finished. | (l/P)/t=rt/t OR (l/P)/t=r |
Solving the equation of a line.There are three equations used for the equation of a line, Slope-Intercept Form, Point-Slope Form and Two Points.Slope-Intercept
| The finished equation is set up in y equals slope (m) mutiplied by x + the y-intercept (b) | y=mx+b |
| To solve, "y" must be isolated from
the rest of the equation.
First, order of operations. |
y-3+-1/2(x-2) OR y-3=-1/2x+1 |
| Then add three to both sides. | y-3+3=-1/2x+1+3 OR y=-1/2x+4 |
| The equation is now in Slope-Intercept From, y is the y-coordinate, -1/2 is the slope, x is the x-coordinate and b is the y intercept. | y=-1/2x+4 |
Point-Slope Form
| The point-slope equation is y minus a y coordinate, equals slope multiplied by x minus a x-coordinate. | y-y1=m(x-x1) |
| To solve the equation, the point and slope is given. | (0,4), m=2 |
| Insert these into the equation. | y-4=2(x-0) |
| If you need to, you can simplify it into mx+b format. Use Order of Operations then add 4 to both sides. | y-4+4=2x+0+4 OR y=2x+4 |
| Now it is in mx=b format. | y+2x+4 |
Two Points
| In this formula, two points are given, and solving it gives you the slope. | (-2,-1) and (3,4) m=y1-y2/x1-x2 |
| Insert these points into the equation. | m=4-(-1)/3-(-2) |
| Solve the addition portion. The remainder is the slope. | m=5/5 OR 1 |
| Simplify into y=mx+b format. Start in Point-Slope form and use one of the points and slope in the equation. | y-(-1)=1(x-(-2)) |
| Add/Subtract numbers. | y+1=1x+2 |
| Add 1 to both sides, to put into y=mx+b format. | y=x+2+1 OR y=x+3 |