Question

If we change the four to a two in the equation what would happen to the graph?

y = 4x + 3

(0,3)
(-0.75,0)

Answer 1

If you change the four to a two in the equation \( y = 4x + 3 \), the new equation becomes:

\[ y = 2x + 3 \]

This change affects the slope of the line represented by the equation.

### Key Differences:

1. **Slope:**
- The original equation \( y = 4x + 3 \) has a slope of 4. This means for every 1 unit increase in \( x \), \( y \) increases by 4 units, making the line steeper.
- The new equation \( y = 2x + 3 \) has a slope of 2. Therefore, for every 1 unit increase in \( x \), \( y \) increases by 2 units, resulting in a less steep line.

2. **Y-Intercept:**
- The y-intercept for both equations remains unchanged at \( (0, 3) \). This is where the line crosses the y-axis.

### Graphical Changes:

- The new graph will still cross the y-axis at the same point (0, 3).
- The intersection with the x-axis will change. For the original equation \( y = 4x + 3 \), setting \( y = 0 \) to find the x-intercept:

\[
0 = 4x + 3 \implies 4x = -3 \implies x = -0.75
\]

Similarly, for the new equation \( y = 2x + 3 \):

\[
0 = 2x + 3 \implies 2x = -3 \implies x = -1.5
\]

### Conclusion:

The graph of \( y = 2x + 3 \) will be less steep than that of \( y = 4x + 3 \) but will intersect the y-axis at the same point and will have a different x-intercept, specifically at \( (-1.5, 0) \) compared to \( (-0.75, 0) \).