Question: The graph of a linear relationship is shown. y x Complete the equation that best represents this graph. Enter numbers in the boxes provided. y= x+ Graph: a straight line with positive slope crossing the y-axis at 3 and the x-axis at -2; position_hint: center

1. **State the problem:** We need to find the equation of a line given its graph. 2. **Identify key points:** The line crosses the y-axis at $3$, so the y-intercept $b=3$. 3. The line crosses the x-axis at $-2$, so the point $(-2,0)$ lies on the line. 4. **Use the slope-intercept form:** The equation of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{-2 - 0} = \frac{-3}{-2} = \frac{\cancel{-3}}{\cancel{-2}} = \frac{3}{2}$$ 6. **Write the equation:** $$y = \frac{3}{2}x + 3$$ 7. **Interpretation:** The slope is positive $\frac{3}{2}$, and the line crosses the y-axis at $3$, matching the graph. **Final answer:** $$y = \frac{3}{2}x + 3$$