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Linear Equations By: Emily Zhou

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**What is a Linear Equation?**

A linear equation is an equation whose graph forms a straight line. Linear equations are usually shown on a coordinate plane Real life situations of linear equations include the stock market as well as the payments of a car.

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**Parts of a Coordinate Plane**

QUADRANT II (-x, y) QUADRANT I (x, y) Origin QUADRANT III (-x, -y) QUADRANT IV (x, -y) X-Axis Y-Axis

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Slope Slope is the ratio of vertical change to the horizontal change (rise/run) of a line. Slope in a linear equation shows if the line is ascending (positive) or descending (negative). Slope can also show the rate of change. The letter m is used to represent slope in a formula.

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**Forms of Linear Equations**

The forms of linear equations are the formats in which the information is written in. These two forms are the most commonly used ways to write linear equations. 1. Slope Intercept Form: y=mx+b 2. Standard Form: Ax + By =C

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**Slope Intercept Form * ¾ is the slope.**

Slope intercept form is y=mx+b. This form makes it easy to find the slope (m) and the y-intercept (b). Working with this form is simple, so it is used more often than other forms. Example: y= ¾x + 3 * ¾ is the slope. * 3 is the point where the line crosses the Y-axis.

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**Graph Using Slope Intercept Form**

I will use the equation y= ½ x-1 to demonstrate how to graph a linear equation using slope intercept form. 1.) First, graph the y-intercept (b). In this equation, b= -1, so place a dot on the point (0,-1). 2.) Next, use the slope (½ ) to rise up once and run twice horizontally. Plot the point. 3.) Plot as many points as desired using the slope, then draw a line through the points. Run 2 Rise 1

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**Standard Form Example: 2x+2y=4**

Standard form for linear equations is Ax + By=C. It can be used to find two points on the line of the equation. Example: 2x+2y=4 1.) Substitute in a zero for x. Simplify. 2(0)+2y=4 y=2 2.) One point of the line is (0,2). Plot the point. 3.) Substitute y with zero. Simplify. 2x+2(0)=4 x=2 4.) The second point is (2,0). Plot it and draw a line through the two points.

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**Using Linear Equations**

Linear equations are not only a main part of algebra courses, but it is just as important in the real world. If you deposited $40 in the bank every year, and you would receive 7% each year, how much will you have in 15 years? Using a linear equation to graph it out, it would give you a better idea about what how much you will have in the future. No matter what kind of situations, linear equations help to make life easier.

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