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Linear equation

Absolute value notes

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1-4, 1-6 Solving Absolute Value Equations and Inequalities Absolute value: distance from zero on a number line. Since distance in a nonnegative, the absolute value of a number is always positive. The symbol lxi is used to represent the absolute value of a number x. I units 4 units I I I I 1 I 3 4 5 Solving Absolute Value Equations: For any real numbers a and b, where b ~! 0, if Jal = then a = b or ?a = b. The second case is often written as a = ?b. Steps 1. Isolate the Absolute Value expression 2. Rewrite equation without the I I symbols. a. One with positive answer b. One with negative answer Ex 1: Jx-51=7 x-c3- ?t-3 k'3 + 3. Solve each equation '7 2\: flL1 - '7 I 2 - \ - 4. Check your answers (plug back into I T

Algebra Fill In Notes 2.7

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02.07 Literal Equations Essential Questions How can you solve linear equations and inequalities in one variable, including equations with coefficients represented by letters? How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations? In the equation: "distance equals rate times time? ____________________ is the most important part. d=(r)(t) In d=(r)(t) the more efficient way to evaluate r is to__________________ it from the rest of the equation first. Work ______________________ to isolate the variable. The key to equations is ________________________.

Algebra Fill In Notes 2.1

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02.01 One-Variable Equations Essential Questions How can we create equations in one variable and use them to solve problems? How can we solve linear equations in one variable? KEEP IT ___________________. The goal is to figure out how much each x weight weighs. You do this by getting one x on one side and its value on the other side. STEPS TO SOLVING AN EQUATION Simplify each side of the __________________. Get the __________________ on one side of the ___________________. Get the _____________ by ___________________. (Solve for the variable) ___________ your solution. Follow along on page 3, Example 1. ?2(x + 1) = 5x + 4 ? x Simplify each side of the equation. Get the variable on one side of the equation.

Point Slope Formula

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Point-slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph. While you could plot several points by just plugging in values of x, the point-slope form makes the whole process simpler. Point-slope form is also used to take a graph and find the equation of that particular line. Point slope form gets its name because it uses a single point on the graph and the slope of the line. Think about it this way: You have a starting point on a map, and you are given a direction to point. You have all the information you need to draw a single line on the map. The standard point-slope equation looks like this:

Slope and y-intercept.

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Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y. The slope m of this line - its steepness, or slant - can be calculated like this: m = change in y-value change in x value Help from math.com

Slope-intercept Form

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Common exercises will give you some pieces of information about a line, and you will have to come up with the equation of the line. How do you do that? You plug in whatever they give you, and solve for whatever you need, like this: Find the equation of the straight line that has slope m = 4 and passes through the point (?1, ?6). Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = ?1 and y = ?6.

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