Graphing Linear Equations by Picking Points

Let’s look at some examples . . . Picking 3 points Given the equation of a line, we know that an ordered pair is on the line if we can substitute its values for the x and y in the equation and get a true statement. To graph a line from an equation, we typically find 3 such points and connect the dots. Let’s look at some examples . . .

Graph: y = 2x + 3 First, we will construct a table of values. x y

Pick values for the complicated side – the one with all the action! Graph: y = 2x + 3 Pick values for the complicated side – the one with all the action! In this example, pick 3 values for x. If you pick an ‘x’ that makes ‘y’ a fraction, pick again!

Pick 3 easy x’s x y 1 -1 Pick numbers near zero so that they’ll fit on your graph!

Find the corresponding y’s y = 2x + 3 x y 3 1 5 -1 ‘cause 3 = 2 ( 0 ) + 3 5 = 2 ( 1 ) + 3 1 = 2 ( -1 ) + 3 Our points are ( 0, 3 ), ( 1, 5 ), ( -1, 1 )

Connect: ( 0, 3 ), ( 1, 5 ), ( -1, 1 ) (1, 5) This is the graph of y = 2x + 3 This is the graph of (0, 3) ( 0, 3 ) ( -1, 1 )

Graph: 3y – 2 = x First, we will construct a table of values. x y

Pick values for the complicated side – the one with all the action! Graph: 3y – 2 = x Pick values for the complicated side – the one with all the action! In this example, pick 3 values for y. If you pick a ‘y’ that makes ‘x’ a fraction, pick again!

Pick 3 easy y’s y x 1 -1 Pick numbers near zero so that they’ll fit on your graph!

Find the corresponding x’s Graph: 3y – 2 = x x y -2 1 -5 -1 ‘cause 3 ( 0 ) - 2 = -2 3 ( 1 ) - 2 = 1 3 ( -1 ) - 2 = -5 Our points are ( -2, 0 ), ( 1, 1 ), ( -5, -1 )

Connect: ( -2, 0 ), ( 1, 1 ), ( -5, -1 ) This is the graph of 3y – 2 = x This is the graph of (1, 1) (-2, 0) (-5, -1)

Graph: 2x + 3y = 5 It is easier to order to construct a table of values, if the equation is solved for either x or y. This equation can be transformed: Add -2x to each side Divide by 3

Pick values for the complicated side – the one with all the action! Graph: Pick values for the complicated side – the one with all the action! In this example, pick 3 values for x. If you pick an ‘x’ that makes ‘y’ a fraction, pick again!

Pick one x that makes y an integer 5/3 1 Nope Hooray! Since the denominator is 3, you may have to try 3 consecutive numbers to find a winner.

Find your other 2 x’s We know that x = 1 gave us a “good” value for y. Since 3 is the denominator, we can get other “good” x values by adding + 3 or - 3 to x = 1. Let’s try 1 + 3 = 4 and 1 – 3 = - 2

Try x = 4 ( 4, -1 ) works!

Try x = -2 ( -2, 3 ) works!

This is a table of the values we’ve found x y 1 4 -1 -2 3 Our points are ( 1, 1 ), ( 4, -1 ), ( -2, 3 )

Connect: ( 1, 1 ), ( 4, -1 ), ( -2, 3 ) (1, 5) This is the graph of ( 1, 5 ) This is the graph of This is the graph of 2x + 3y = 5 (-2,3) (0, 3) ( 0, 3 ) (1, 1) ( -1, 1 ) (4,-1)

When asked to graph the equation of a line by plotting points: Solve for either x or y Pick 3 values for the letter that’s on the “complicated” side. Calculate the corresponding value for the other letter. Skip numbers that give you fractions. Plot the points Connect the dots!