Graphing Linear Equations by Picking Points Picking 3

Graphing Linear Equations by Picking Points

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

Graph: y = 2 x + 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 0 1 -1 y Pick numbers near zero so that they’ll fit on your graph!

Find the corresponding y’s y = 2 x + 3 x 0 1 -1 y 3 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, 1, 5 5) ) ( (0, 0, 3 3) ) This is the graph of y = 2 x + 3 ( -1, 1 )

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

Graph: 3 y – 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 0 1 -1 x Pick numbers near zero so that they’ll fit on your graph!

Find the corresponding x’s Graph: 3 y – 2 = x x -2 1 -5 y 0 1 -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 ) (1, 1) (-2, 0) (-5, -1) This is the graph of 3 y – 2 = x

Graph: 2 x + 3 y = 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 -2 x to each side Divide by 3

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 x y 0 5/3 1 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 -2 1 -1 3 Our points are ( 1, 1 ), ( 4, -1 ), ( -2, 3 )

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

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!