Question

Which graph matches the equation y+3=2(x+3)?

Answer 1

To determine which graph matches the equation \( y + 3 = 2(x + 3) \), we can first rewrite the equation in slope-intercept form (i.e., \( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the given equation:

\[
y + 3 = 2(x + 3)
\]

Distributing the 2 on the right side:

\[
y + 3 = 2x + 6
\]

Next, isolate \( y \) by subtracting 3 from both sides:

\[
y = 2x + 6 - 3
\]

This simplifies to:

\[
y = 2x + 3
\]

Now, we can identify key features of the line:

- The slope \( m = 2 \), which means that for every 1 unit increase in \( x \), \( y \) increases by 2 units.
- The y-intercept \( b = 3 \), which means the line crosses the y-axis at (0, 3).

To find the x-intercept, set \( y = 0 \):

\[
0 = 2x + 3 \\
2x = -3 \\
x = -\frac{3}{2}
\]

So the x-intercept is at \((-1.5, 0)\).

Now you can look at the graphs available to find one that has:
- A slope of 2 (meaning it rises steeply),
- A y-intercept at (0, 3), and
- An x-intercept at \((-1.5, 0)\).

If you have a set of graphs to choose from, look for these characteristics to identify the correct one.