5-4: Graphing Linear Equations OBJECTIVE: You will graph linear equations by making a table of values. So what is a linear equation anyway? It is an equation whose graph is a line. In the previous section, we had several graphs that looked like this: We were taking the domain that was given, finding the range for each domain, and plotting the resulting ordered pairs. Do you notice any type of pattern associated with the blue dots on the graph? You can draw a single line through all of them. All these points lie on the same line. Are there any points in-between these points on the graph? YES -These are points of a linear equation.

5.3.4 DEFINITION OF A LINEAR EQUATION IN STANDARD FORM 5-4: Graphing Linear Equations Linear equations may contain one or two variables with no variable having an exponent other than 1. A linear equation is an equation that can be written in the form Ax + By = C, where A, B, and C are any real numbers, and A and B are not both zero. 5.3.4 DEFINITION OF A LINEAR EQUATION IN STANDARD FORM The first type of problem you will face is identifying if an equation is linear or not. Hint: If it has powers on the variables, the answer is no.

5-4: Graphing Linear Equations EXAMPLE 1: Determine whether each equation is a linear equation. If so, identify A, B, and C. A. 4x = 7 + 2y B. 2x2 - y = 7 C. x = 12 4x = 7 + 2y First, rewrite so variables are on the same side of the equation. -2y - 2y This equation is in the form Ax + By = C. No powers, so it is linear. A = 4, B = -2, C = 7 4x - 2y = 7 The x-variable has a power of 2 on it. If there are any variables with powers over one, the equation is not linear. Therefore, this equation is not linear. No powers on the letters. Yes, the y is missing, but this is still going to be a line. A = 1 B = 0 (because the y-variable is missing) C = 12

5-4: Graphing Linear Equations When the book had us graph relations, they chose the domain we had to work with. We had no choice and were limited to a few specific points on our graphs. Now, though, we need to be looking at any possible value of the domain that can go into the equation. Since the domain can be many, many numbers, simply drawing points will not do for the graph. What happens is the space between points collapses and forms a line.

5-4: Graphing Linear Equations In these problems that you must graph, you get to choose a few values for the domain to plug into a table. Then plug in the domain and find the corresponding range. Write the ordered pairs and graph them. Now we connect the dots to represent all those other points in-between that you could have chosen. Draw the lines going to infinity in both directions to represent the other points you could have chosen. Technically, you only need 2 points to make a line. However, three can give you a little double-check on your work - so choose three domains to plug in.

5-4: Graphing Linear Equations EXAMPLE 2: Graph the equation y = 3x - 4. Choose five values for the domain. Plug them into a table. Plot the points on a graph. Draw a line through the points to finish. Make sure arrows are on both ends! Figure out the range for each domain. Write the ordered pairs. x -1 1 2 3 3x - 4 3(-1) - 4 3(0) - 4 3(1) - 4 3(2) - 4 3(3) - 4 y -7 -4 -1 2 5 (x, y) (-1, -7) (0, -4) (1, -1) (2, 2) (3, 5) The line is the visual representation of the equation. The line is also your answer to this problem.

5-4: Graphing Linear Equations EXAMPLE 3: Graph the equation 2x + 5y = 10. In order to find values for y more easily, solve the equation for y. 2x + 5y = 10 -2x -2x 5y = 10 - 2x 5 5 Now plot the points and draw a line through them for the answer. Since there is a 2/5 multiplied by each x, choosing values of x which are divisible by five will make the problem easier. The y-values will end up being whole numbers rather than fractions. So, now we choose our x-values and make a table. In my table, I have to use 0.4.

5-4: Graphing Linear Equations HOMEWORK Page 283 #17 - 35 odd