Question

Which graph represents the equation y = x – 3?
On a coordinate plane, a line goes through points (negative 3, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).
On a coordinate plane, a line goes through points (0, negative 3) and (3, 0).

Answer 1

To determine which graph represents the equation \( y = x - 3 \), we can analyze the equation itself.

The equation \( y = x - 3 \) is in slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope (which is 1 in this case),
- \( b \) is the y-intercept (which is -3 in this case).

This means that the line crosses the y-axis at \( (0, -3) \).

Next, we can find another point on the line by substituting a value for \( x \). If \( x = 3 \):
\[
y = 3 - 3 = 0
\]
This means that the line also passes through the point \( (3, 0) \).

Now let's review the options given:

1. **First option**: A line through points \( (-3, 0) \) and \( (0, -3) \).
- The y-intercept here is \( -3 \), but it does not go through \( (3, 0) \).

2. **Second option**: A line through points \( (0, -1) \) and \( (1, 2) \).
- The y-intercept is \( -1 \) and the slope is 3, so this does not represent the equation.

3. **Third option**: A line through points \( (0, -3) \) and \( (3, 0) \).
- This option has the correct y-intercept of \( -3 \) and passes through the point \( (3, 0) \).

Thus, the graph that represents the equation \( y = x - 3 \) is the **third option**, which goes through points \( (0, -3) \) and \( (3, 0) \).