What do you know about linear equations? Do you think linear equations are functions? Write it down on your board Share with your shoulder partner Graphing Linear Equations

y = mx + b We can also see this equation as y = b+mx Or, y = ax + b To graph a linear equation, we first need to rewrite the equation in function form. This is also known as Slope-Intercept Form

Every variable means something in y = mx + b The y represents:  Range, output, and dependent variable and all the solutions that makes the equation true. The x represents:  Domain, input, independent variable and all the solutions that makes the equation true. The m represents: the slope. The steepness of the line and whether it will be positive, negative, zero or undefined. The b represents: the y-intercept or where the line or equation crosses the y axis.

Identify the slope and the y- intercept (b) 1. y = 4x +3 Slope=4 y-intercept = 3 2. y = -3x -2 Slope = -3 y-intercept = y = 1/2x + 6 Slope = ½ y-intercept = 6

Let’s practice writing an equation in slope-intercept form! Using y = mx + b If I said that m = 4 and b = 6, would you be able to write an equation in slope intercept form? Write it on your board, then show your face partner.

Check your answer! Did you get: y = 4x + 6

Try a few more! 1.m = 5 b = 2 2.m = 3 b = 8 3.m = 1 b = 2

Check your answers! 1.y = 5x y = 3x y = 1x + 2 but as we learned earlier we usually do not need to show the coefficient 1, it is understood so, we write it as: y = x +2

Try a few more! 1.b = 2 m = 3 2.m = -3 b = 5 3.m = 4 b = -2 4.m = 0 b = 4

Check your answers! 1.y = 3x y = -3x y = 4x y = 0x + 4, but we know that 0 times anything = 0, so it is written as: y = 4

What do you think the slope of the equation means? Discuss with your shoulder partner. The slope indicates the direction (positive, negative, undefined or zero slope) as well as steepness or slant. So, in the equation y=2x+4, the slope is 2 and since the 2 is positive, that means the graph will lean in the positive direction. The 4 represents where the graph will cross the y- axis at positive 4.

What does a positive slope look like, and what does it mean? A positive slope: That means that when the value of one is increasing, so is the other. This slope rises from left to right.

The equations y = -3x +4 Since the slope is -3, that means that the graph will lean in the negative direction, and will intersect the y-axis at positive 4.

What does a negative slope look like, and what does that mean? A negative slope looks like: That means one is increasing, the other is decreasing. This one falls from left to right.

There are two other lines we will discuss later. Zero slope which is also called a y=b and when ordered pairs are graphed create a horizontal line: Undefined slope which is an x=a and when ordered pairs are graphed create a vertical line :

Now that we have mastered that, we are ready! We need to solve for y, so that the equation will be in slope-intercept form. Take the equation y + 2 = 3x y = 3x -2

-3x + y = 12 Write it on your dry erase board and share with your shoulder partner! Now you try one!

Did you get? y = 3x + 12? Lets look at it: We started with: -3x + y = 12 +3x +3x y = 3x + 12

1.5x + 5y = 19 Remember, we are trying to write it in slope-intercept form, so we need to solve for y and y needs to be on the left side of the equals sign! We need to try one that is a little more challenging!

Here we go! 5x + 5y = 19 -5x -5x 5y = -5x y = - 5x or y = -x

1.2x + 3y = 6 2.X + 4y = x – y = 5 (y needs to be positive when complete) Try these and share with your shoulder partner.

1.y = 2/3x y = -1/4x y = -x - 5 Check your answers!

Once they are in slope-intercept form, we can substitute values in for x, solve the equation to get the y. Example: y = 2x + 4 Pick a number, 1 to substitute in for x. So, y = y = 2+4 y = 6 xy y = 2x So we have ordered pairs {(1,6),(2,8),(3,10),(4,12),(5,14)}

Try one yourself! y = -3x +4 I am going to pick the numbers: to substitute in for x. And solve for y. xy So we have ordered pairs {(0,4), (1, 1), (2, -2), (3,-5)}