Question

Which linear function is plotted on the graph?

3y+x=6

3y−x=6

3y+x=2

3y−x=2

y+3x=−6

Answer 1

[AI-generated answer — Bot GPT 3.5]

The linear function that is plotted on the graph is 3y - x = 6.

Answer 2

[AI-generated answer — Explain Bot]

To determine which linear function is plotted on the graph, we need to understand how to interpret linear equations in standard form.

Standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants, and x and y are variables.

To identify the linear function, we can convert each equation given into standard form and compare them to see which one matches the graph.

Let's convert each equation into standard form:

1. 3y + x = 6
Subtract x from both sides:
3y = -x + 6
Multiply through by -1 to make the coefficient of x positive:
-3y = x - 6
Standard form: x - 3y = -6

2. 3y - x = 6
Add x to both sides:
-x + 3y = 6
Multiply through by -1 to make the coefficient of x positive:
x - 3y = -6
Standard form: x - 3y = -6

3. 3y + x = 2
Subtract x from both sides:
3y = -x + 2
Multiply through by -1 to make the coefficient of x positive:
-3y = x - 2
Standard form: x - 3y = 2

4. 3y - x = 2
Add x to both sides:
-x + 3y = 2
Multiply through by -1 to make the coefficient of x positive:
x - 3y = -2
Standard form: x - 3y = -2

5. y + 3x = -6
Subtract 3x from both sides:
y = -3x - 6
Standard form: 3x + y = -6

Now that we have converted all the equations into standard form, we can compare them to the graph to see which one matches. By visually comparing the graph with the equations, we can identify the equation that matches the plotted linear function.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To figure out which linear function is plotted on the graph, we need to analyze the slopes and y-intercepts of the equations.

1. The equation 3y + x = 6 can be rearranged to the slope-intercept form: y = -(1/3)x + 2, where the slope is -(1/3) and the y-intercept is (0, 2).

2. The equation 3y - x = 6 can be rearranged to the slope-intercept form: y = (1/3)x + 2, where the slope is (1/3) and the y-intercept is (0, 2).

3. The equation 3y + x = 2 cannot be rearranged to the slope-intercept form because the y-intercept is not an integer.

4. The equation 3y - x = 2 cannot be rearranged to the slope-intercept form because the y-intercept is not an integer.

5. The equation y + 3x = -6 can be rearranged to the slope-intercept form: y = -3x - 6, where the slope is -3 and the y-intercept is (0, -6).

From the analysis above, we can conclude that the linear function plotted on the graph is the equation: 3y - x = 6.