How do you graph # y + 1/3x = 2# by plotting points?

Question

Abigail Allen · Accepted Answer

Please see below.

As the coefficient of #x# is #1/3#, let us pick three values of #x# which are multiple of #3# and let these be #-9,0# and #9#. For these corresponding values of #y# will be #y+1/3(-9)=2# or #y-3=2# or #y=5# #y+1/3(0)=2# or #y=2# #y+1/3(9)=2# or #y+3=2# or #y=-1# Hence, three points through which #y+1/3x=2# passes are #(-9,5)#, #(0,2)# and #(9,-1)#. Joining these points gives us the graph of #y+1/3x=2# graph{y+1/3x=2 [-6.84, -3.16, 10.08, 9.92]}

Hazel Anglin · Answer

For an equation like this you choose two values for x and calculate y, then trace the line between these two points.

For the sake of simplicity, let me select x=0 and x=6. Entering these values into the equation, I obtain y=2 for x=0 and y=0 for x=6. Now remember that this only works for linear functions. Also, in this particular case, because of the division by 3, it is easy to see that choosing values for x that are multiples of 3 will be easier to calculate the results, so while you CAN choose any value for x to plot, choosing the values carefully will help with the calculations. Just as another example looking at the graph, I see that: #if x=3# then # y=1# # if x=9# then #y=-1# and #if x=-3# then #y=4#... The following graph displays the tho points (0,2) and (6,0): graph{y+1/3x=2 [-10, 10, -5, 5]}

Julia Adams · Answer

undefined To graph the equation $ y + \frac{1}{3}x = 2 $ by plotting points, you can choose arbitrary values for x and then calculate the corresponding values for y using the equation. For example, you can choose x = 0, x = 3, and x = 6. Then, calculate the corresponding y-values using the equation $ y + \frac{1}{3}x = 2 $. Plot these points on a coordinate plane and connect them to form a straight line. Repeat this process for additional points if needed to accurately depict the graph.

Eli Assouline · Answer

undefined To graph the equation y + (1/3)x = 2 by plotting points, follow these steps:

1. Choose values for x.
2. Substitute each chosen value of x into the equation to find the corresponding values of y.
3. Plot the points (x, y) on the coordinate plane.
4. Connect the points to form the graph.

Here's an example:

Let's choose three values for x: -3, 0, and 3.

When x = -3:
y + (1/3)(-3) = 2
y - 1 = 2
y = 3

So, when x = -3, y = 3. Plot the point (-3, 3).

When x = 0:
y + (1/3)(0) = 2
y = 2

So, when x = 0, y = 2. Plot the point (0, 2).

When x = 3:
y + (1/3)(3) = 2
y + 1 = 2
y = 1

So, when x = 3, y = 1. Plot the point (3, 1).

Connect the points (-3, 3), (0, 2), and (3, 1) to form the graph of the equation y + (1/3)x = 2.