Graphing and Equations Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

Important Information When graphing a linear equation, you need to know the slope and the y-intercept The slope is the rate of change in your graph or how the y values change as x increases The y-intercept is the place where the graph crosses the y-axis The general form of a linear equation is y = a + bx where a is the y-intercept and b is the slope

Slope There are many different ways to represent the slope. change in y ; ; change in x If the line is increasing from left to right, the slope is positive If the line is decreasing from left to right, the slope is negative

Slope The numerator (top number in the fraction) will tell you how much to move up or down The denominator (bottom number in the fraction) will tell you how much to move left or right If the slope is positive, start at the y-intercept and move up and to the right or down and to the left If the slope is negative, start at the y-intercept and move up and to the left or down and to the right

Slope Look at the following fractions to see why you move in specific directions for positive or negative slopes. OR OR

Y-Intercept When looking for the y-intercept, you should follow the line until it hits the y-axis If the line crosses above the x-axis, the y-intercept is positive If the line crosses below the x-axis, the y-intercept is negative

Making the Graph Given the Equation The slope will always be the value with the x-term so in this case, the slope is… Let’s take a look at the following equation. What are the slope and y-intercept?

Making the Graph Given the Equation The y-intercept will be the number that stands alone (not with the x term) so in this case the y-intercept is… Let’s take a look at the following equation. What are the slope and y-intercept?

Making the Graph Given the Equation Now that we know the slope and y-intercept, we can graph the equation.

Making the Graph Given the Equation First you’ll need to plot the y-intercept. Put a point at 2 on the y-axis.

Making the Graph Given the Equation The numerator is the change in y and the denominator is the change in x. Next, you’ll need to find another point on the line using the slope.

Making the Graph Given the Equation Since the slope is positive, you can find the next point by moving up and to the right or down and to the left.

Making the Graph Given the Equation Start at the y intercept and go up 3 then to the right 5 and put a point.

Making the Graph Given the Equation You can also start at the y intercept and go down three then to the left 5 and put a point.

Making the Graph Given the Equation Now connect these points with a line. Your line should go through all the points you plotted and continues through the entire graph.

Making the Graph Given the Equation Be sure to label the line with your y= equation.

Making the Graph Given the Equation Let’s try another example… What is the slope? In this case, the slope is -2 because that is the value with the x-term. Be very careful to always include the sign when you are finding slope. Again, our first step is to find the slope and y-intercept.

Making the Graph Given the Equation Let’s try another example… What is the y-intercept? The y-intercept is 4 because that is the number that stands alone. Again, our first step is to find the slope and y-intercept.

Making the Graph Given the Equation Now we can graph the equation! Plot a point at the y-intercept.

Making the Graph Given the Equation Since the slope is a whole number, we need to change it to a fraction. How would you write -2 as a fraction?

Making the Graph Given the Equation -2 is equal to Now we need to plot the next point.

Making the Graph Given the Equation -2 is equal to Start at the y-intercept and go down 2 then to the right 1 and plot a point

Making the Graph Given the Equation -2 is equal to You could also go up 2 then to the left 1 and plot a point

Making the Graph Given the Equation Now draw a line to connect the points.

Making the Graph Given the Equation Again, be sure to label the line with the equation.

Making the Equation Given the Graph When you are given then graph, you’ll need to find the y-intercept and the slope. Where does the line touch the y-axis?

Making the Equation Given the Graph The graph crosses the y-axis at 5. Therefore, the y-intercept is 5.

Making the Equation Given the Graph Next, you’ll need to find the slope. Remember to look for “points in corners”

Making the Equation Given the Graph The first point in a corner is at your y-intercept (0, 5). Find another point in a “corner”.

Making the Equation Given the Graph The next point in a corner is (1, 1). Now find the slope between these two points.

Making the Equation Given the Graph (0, 5) and (1, 1) You can use the slope formula above to find the slope.

Making the Equation Given the Graph (0, 5) and (1, 1)

Making the Equation Given the Graph Now you know the slope and y-intercept so you can find your equation. Remember the general form of a line is

Making the Equation Given the Graph So, the equation of the line is

Making the Equation Given the Graph Let’s try another example. First, you’ll need to find the y-intercept. In this case, the y-intercept is -2.

Making the Equation Given the Graph Next, you’ll need to find the slope. You can use the slope formula or you can use the graph to find the change in y and the change in x.

Making the Equation Given the Graph We already have the y-intercept as our first point in a corner. Now we need to find another point in a “corner”.

Making the Equation Given the Graph (3, 1) is a point in a “corner”. Let’s use the triangle method to find the slope between these two points.

Making the Equation Given the Graph Starting from the y-intercept, you need to draw a triangle between your two points in “corners”.

Making the Equation Given the Graph What is the difference in your y values? 3 3 What is the difference in your x values?

Making the Equation Given the Graph So your slope is 3 3

Making the Equation Given the Graph We can plug the slope and y-intercept into the general equation of a line.

Follow-Up Questions Answer the following questions on loose leaf and hand them in to your teacher.

Follow-Up Questions Graph the following equations. Be sure to label each line. a) d) b) e) c)

Follow-Up Questions 2. Find the equations to the given graphs. a) b)

Follow-Up Questions c) d)

Follow-Up Questions e)