Graphing the equation

To graph the equation 2x + 3y = 11, we need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Let's solve the equation for y:

2x + 3y = 11
3y = -2x + 11
y = (-2/3)x + 11/3

Now we have the equation in slope-intercept form. The slope of the line is -2/3, and the y-intercept is 11/3.

We can start graphing the equation by plotting the y-intercept, which is the point (0, 11/3).

Finding additional points

To find more points on the graph, we can choose different values for x and substitute them into the equation to get the corresponding y-values. Let's choose two more values for x and find the corresponding y-values:

When x = 1:
y = (-2/3)(1) + 11/3
y = -2/3 + 11/3
y = 9/3
y = 3

So, when x = 1, y = 3. This gives us the point (1, 3) on the graph.

When x = -1:
y = (-2/3)(-1) + 11/3
y = 2/3 + 11/3
y = 13/3

So, when x = -1, y = 13/3. This gives us the point (-1, 13/3) on the graph.

Plotting the points and drawing the line

Now, we can plot the points (0, 11/3), (1, 3), and (-1, 13/3) on a coordinate plane and connect them to draw the line.

The graph should show a line passing through these three points.

Finding the value of y when x = 1

From the graph, we can see that when x = 1, the corresponding y-value is approximately 3.

Therefore, when x = 1, y ≈ 3.

Conclusion

The graph of the equation 2x + 3y = 11 is a line with a slope of -2/3 and a y-intercept of 11/3. By plotting points and connecting them, we can draw the line. From the graph, we can determine the value of y when x = 1, which is approximately 3.