<< Chapter < Page Chapter >> Page >

Graph the equation 3 x + y = −1 .

Solution

Find three points that are solutions to the equation. 3 x + y = −1 First solve the equation for y . y = −3 x 1

We’ll let x be 0, 1, and −1 to find 3 points. The ordered pairs are shown in [link] . Plot the points, check that they line up, and draw the line. See [link] .

3 x + y = −1
x y ( x , y )
0 −1 ( 0 , −1 )
1 −4 ( 1 , −4 )
−1 2 ( −1 , 2 )
The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (negative 1, 2), (0, negative 1), and (1, negative 4). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation 3x plus y equals negative 1.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph the equation 2 x + y = 2 .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 2, 6), (0, 2), (2, negative 2), (4, negative 6), and (6, negative 10). The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

Graph the equation 4 x + y = −3 .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 9), (negative 2, 5), (negative 1, 1), (0, negative 3), (1, negative 7), and (2, negative 10). The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

If you can choose any three points to graph a line, how will you know if your graph matches the one shown in the answers in the book? If the points where the graphs cross the x - and y -axis are the same, the graphs match!

The equation in [link] was written in standard form, with both x and y on the same side. We solved that equation for y in just one step. But for other equations in standard form it is not that easy to solve for y , so we will leave them in standard form. We can still find a first point to plot by letting x = 0 and solving for y . We can plot a second point by letting y = 0 and then solving for x . Then we will plot a third point by using some other value for x or y .

Graph the equation 2 x 3 y = 6 .

Solution

Find three points that are solutions to the equation. 2 x 3 y = 6 First let x = 0 . 2 ( 0 ) 3 y = 6 Solve for y . −3 y = 6 y = −2 Now let y = 0 . 2 x 3 ( 0 ) = 6 Solve for x . 2 x = 6 x = 3 We need a third point. Remember, we can choose any value for x or y . We’ll let x = 6 . 2 ( 6 ) 3 y = 6 Solve for y . 12 3 y = 6 −3 y = −6 y = 2

We list the ordered pairs in [link] . Plot the points, check that they line up, and draw the line. See [link] .

2 x 3 y = 6
x y ( x , y )
0 −2 ( 0 , −2 )
3 0 ( 3 , 0 )
6 2 ( 6 , 2 )
The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (0, negative 2), (3, 0), and (6, 2). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation 2x minus 3y equals 6.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph the equation 4 x + 2 y = 8 .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

Graph the equation 2 x 4 y = 8 .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative 5), (negative 4, negative 4), (negative 2, negative 3), (0, negative 2), (2, negative 1), (4, 0), and (6, 1). The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

Graph vertical and horizontal lines

Can we graph an equation with only one variable? Just x and no y , or just y without an x ? How will we make a table of values to get the points to plot?

Let’s consider the equation x = −3 . This equation has only one variable, x . The equation says that x is always equal to −3 , so its value does not depend on y . No matter what y is, the value of x is always −3 .

So to make a table of values, write −3 in for all the x values. Then choose any values for y . Since x does not depend on y , you can choose any numbers you like. But to fit the points on our coordinate graph, we’ll use 1, 2, and 3 for the y -coordinates. See [link] .

x = −3
x y ( x , y )
−3 1 ( −3 , 1 )
−3 2 ( −3 , 2 )
−3 3 ( −3 , 3 )

Plot the points from [link] and connect them with a straight line. Notice in [link] that we have graphed a vertical line .

The figure shows a vertical straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (negative 3, 1), (negative 3, 2), and (negative 3, 3). A vertical straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation x equals negative 3.

Vertical line

A vertical line    is the graph of an equation of the form x = a .

The line passes through the x -axis at ( a , 0 ) .

 

Graph the equation x = 2 .

Solution

The equation has only one variable, x , and x is always equal to 2. We create [link] where x is always 2 and then put in any values for y . The graph is a vertical line passing through the x -axis at 2. See [link] .

x = 2
x y ( x , y )
2 1 ( 2 , 1 )
2 2 ( 2 , 2 )
2 3 ( 2 , 3 )
The figure shows a straight vertical line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (2, 1), (2, 2), and (2, 3). A vertical straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation x equals 2.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph the equation x = 5 .

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

Graph the equation x = −2 .

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 1), (negative 2, 2), (negative 2, 3), and all other points with first coordinate negative 2. The line has arrows on both ends pointing to the outside of the figure.

Got questions? Get instant answers now!

What if the equation has y but no x ? Let’s graph the equation y = 4 . This time the y - value is a constant, so in this equation, y does not depend on x . Fill in 4 for all the y ’s in [link] and then choose any values for x . We’ll use 0, 2, and 4 for the x -coordinates.

y = 4
x y ( x , y )
0 4 ( 0 , 4 )
2 4 ( 2 , 4 )
4 4 ( 4 , 4 )

The graph is a horizontal line passing through the y -axis at 4. See [link] .

Questions & Answers

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin Reply
y=2×+9
Jacob Reply
Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?
Hector Reply
Mayra has $124 in her checking account. She writes a check for $152. What is the New Balance in her checking account?
REVOLUTION Reply
-28$
ashley
-$28
Stephanie
Practice Key Terms 3

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask