Question

graph y = 2 (5 - 3x) - 6 + 9x

Answer 1

To graph the equation \( y = 2(5 - 3x) - 6 + 9x \), we first need to simplify it.

1. Distribute the \( 2 \):
\[
y = 2 \times 5 - 2 \times 3x - 6 + 9x
\]
\[
y = 10 - 6x - 6 + 9x
\]

2. Combine like terms:
\[
y = 10 - 6 - 6x + 9x
\]
\[
y = 4 + 3x
\]

Now we have the simplified equation:
\[
y = 3x + 4
\]

### Step to Graph the Equation

1. **Identify the y-intercept**:
The y-intercept occurs when \( x = 0 \):
\[
y = 3(0) + 4 = 4
\]
So the y-intercept is \( (0, 4) \).

2. **Identify the slope**:
The slope is 3, meaning for every unit increase in \( x \), \( y \) increases by 3. This indicates the line rises steeply.

3. **Plot the y-intercept** at \( (0, 4) \).

4. **Use the slope to find another point**:
Starting from \( (0, 4) \), move up 3 units and to the right 1 unit to find another point:
\( (1, 7) \) because:
\[
y = 3(1) + 4 = 3 + 4 = 7
\]

5. **Plot the second point** at \( (1, 7) \).

6. **Draw a straight line** through the points \( (0, 4) \) and \( (1, 7) \).

### Summary:
The graph of the equation \( y = 3x + 4 \) is a straight line with a y-intercept of 4 and a slope of 3, rising from left to right.