Copy and complete the table of values below for the relations-3x+4:x=-4,-3,-2,-1,0,1,2, Y=-3,-5,....1,...,...,0. Using a scale of 2cm to 1unit on the x-axis and 2cm to 1unit on the y-axis.plot the graph of y-3x+4
To complete the table of values, we need to substitute the given x-values into the equation y = -3x + 4 to find the corresponding y-values:
For x = -4: y = -3(-4) + 4 = 16
For x = -3: y = -3(-3) + 4 = 13
For x = -2: y = -3(-2) + 4 = 10
For x = -1: y = -3(-1) + 4 = 7
For x = 0: y = -3(0) + 4 = 4
For x = 1: y = -3(1) + 4 = 1
For x = 2: y = -3(2) + 4 = -2
Now we can complete the table:
| x | y |
| --- | --- |
| -4 | 16 |
| -3 | 13 |
| -2 | 10 |
| -1 | 7 |
| 0 | 4 |
| 1 | 1 |
| 2 | -2 |
To plot the graph, we will use the given scale of 2cm to 1 unit on both axes.
First, we'll mark the x-axis from -4 to 2, with 2cm spacing between each unit.
Then, we'll mark the y-axis from 16 to -2, with 2cm spacing between each unit.
Now, for each coordinate (x, y), we find the point on the graph by counting the units from the origin and plotting the corresponding point.
The graph of the equation y = -3x + 4 will pass through the following points:
(-4, 16)
(-3, 13)
(-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2, -2)
Now, connect these points with a line:
|
|
|
^ |
│ |
│ |
│ |
├───┼───┼───┼───┼───┼───
│ │ │ │ │ │ │ │
-4 -3 -2 -1 0 1 2
The graph of y = -3x + 4 is a straight line that passes through these points.
To complete the table and plot the graph, we will substitute each value of x into the given equation to find the corresponding y values.
Let's start by completing the table:
| x | y |
|----|----|
| -4 | 7 |
| -3 | 13 |
| -2 | 19 |
| -1 | 25 |
| 0 | 31 |
| 1 | 37 |
| 2 | 43 |
Now, let's plot the points on a graph. Since the scale is 2cm to 1 unit on both axes, each unit will be represented by a 2cm interval.
Draw the coordinate axes with proper intervals and labels for x and y. Then, plot the points (-4, 7), (-3, 13), (-2, 19), (-1, 25), (0, 31), (1, 37), and (2, 43) on the graph.
Next, connect the points with a straight line to create the graph. The equation of the line is y = 3x + 4. Make sure the line contains all the plotted points.
Your completed graph should resemble a line slanting upwards from left to right.
I hope this helps! Let me know if you have any further questions.
To complete the table of values, we need to substitute the given values of x into the equation y = -3x + 4 and calculate the corresponding values of y.
Let's substitute the given values of x into the equation:
For x = -4:
y = -3(-4) + 4
y = 12 + 4
y = 16
For x = -3:
y = -3(-3) + 4
y = 9 + 4
y = 13
For x = -2:
y = -3(-2) + 4
y = 6 + 4
y = 10
For x = -1:
y = -3(-1) + 4
y = 3 + 4
y = 7
For x = 0:
y = -3(0) + 4
y = 0 + 4
y = 4
For x = 1:
y = -3(1) + 4
y = -3 + 4
y = 1
For x = 2:
y = -3(2) + 4
y = -6 + 4
y = -2
Now, let's complete the table of values:
x | y
-----------
-4 | 16
-3 | 13
-2 | 10
-1 | 7
0 | 4
1 | 1
2 | -2
Now, we have the values for the x and y coordinates. We can use a scale of 2cm to 1 unit on both the x-axis and y-axis to plot the graph of y = -3x + 4.
To plot the points on the graph, mark the points on the x-axis and y-axis according to the values in the table.
For example:
- For (x = -4, y = 16), mark the point (-4, 16).
- For (x = -3, y = 13), mark the point (-3, 13).
- Repeat this for all the points.
Once all the points are marked, connect them with a straight line to create the graph of y = -3x + 4.