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.