Question

graph the line represented by the equation 2x+3y=6.
where would the points go on the graph. pick wo points that'll make a line connect.

Answer 1

what value of m makes the equation 2/3(m-9)=1/3(m-27) true?

Responses:
-9
-3
-1
-6

Answer 2

To graph the line represented by the equation \(2x + 3y = 6\), we can first find two points on the line. We can do this by picking values for \(x\) and solving for \(y\), or vice versa.

### Finding Points

1. **Find intercepts**:
- **\(x\)-intercept**: Set \(y = 0\) and solve for \(x\):
\[
2x + 3(0) = 6 \implies 2x = 6 \implies x = 3
\]
So, the \(x\)-intercept is \((3, 0)\).

- **\(y\)-intercept**: Set \(x = 0\) and solve for \(y\):
\[
2(0) + 3y = 6 \implies 3y = 6 \implies y = 2
\]
So, the \(y\)-intercept is \((0, 2)\).

### Points for the Line

From the calculations above, two points that lie on the line \(2x + 3y = 6\) are:
- Point 1: \((3, 0)\)
- Point 2: \((0, 2)\)

### Plotting Points

1. **Point (3, 0)**: On the graph, place a point at \(x = 3\) and \(y = 0\) (which is on the x-axis).
2. **Point (0, 2)**: On the graph, place a point at \(x = 0\) and \(y = 2\) (which is on the y-axis).

### Drawing the Line

Once you have plotted both points:
- Draw a straight line through the points \((3, 0)\) and \((0, 2)\).

This line represents the equation \(2x + 3y = 6\). To summarize:
- Two points to connect are \((3, 0)\) and \((0, 2)\).