make a table and graph the function y=x+3
x | y
-2 | 1
-1 | 2
0 | 3
1 | 4
2 | 5
Graph:
\begin{tikzpicture}
\draw[->] (-3,0) -- (3,0) node[right] {$x$};
\draw[->] (0,-3) -- (0,3) node[above] {$y$};
\draw[color=blue] (-2,1) -- (-1,2) -- (0,3) -- (1,4) -- (2,5);
\end{tikzpicture}
To create a table and graph of the function y = x + 3, you will need to choose some values for x, plug them into the equation, calculate the corresponding values for y, and then plot these points on a graph.
Let's choose five values for x to create the table:
1. x = 0:
y = 0 + 3 = 3
2. x = 1:
y = 1 + 3 = 4
3. x = -1:
y = -1 + 3 = 2
4. x = 2:
y = 2 + 3 = 5
5. x = -2:
y = -2 + 3 = 1
Table:
| x | y |
|-----|-----|
| 0 | 3 |
| 1 | 4 |
| -1 | 2 |
| 2 | 5 |
| -2 | 1 |
Now, let's plot these points on a graph:
1. Draw a set of axes, labeling the x-axis and y-axis.
2. Plot the points from the table on the graph. For example, the point (0, 3) would be plotted at the location where x = 0 and y = 3. Similarly, plot the other points accordingly.
3. Once you have plotted all the points, draw a straight line through them. Since the equation is y = x + 3, the line will be a straight line with a slope of 1 (which means for every 1 unit increase in x, the corresponding y-value increases by 1) and intersects the y-axis at 3.
Your graph of the function y = x + 3 should now be complete.
To create a table and graph the function y = x + 3, we will list a few values of x and calculate the corresponding values of y.
Table:
_____________________
| x | y |
---------------------
| -3 | 0 |
| -2 | 1 |
| -1 | 2 |
| 0 | 3 |
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
---------------------
Graph:
Now, we will plot these points on a graph:
|
7 | .
| .
6 | .
| .
5 |
|
4 | .
|
3 | .
| .
2 | .
|
1 | .
|
0 |_____________________
-3 -2 -1 0 1 2 3
Note that the dots represent the plotted points on the graph. The x-axis represents the values of x, and the y-axis represents the corresponding values of y.