Line Graph Identification 4Ea246

1. **State the problem:** We need to determine which graph correctly represents the equation $$y = 2x - 3$$. 2. **Recall the form and properties:** The equation is in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Identify slope and intercept:** Here, $$m = 2$$ (positive slope) and $$b = -3$$ (y-intercept below zero). 4. **Interpret the slope:** A positive slope means the line rises from left to right. 5. **Interpret the y-intercept:** The line crosses the y-axis at $$-3$$, which is below zero. 6. **Find the x-intercept:** Set $$y=0$$ to find x-intercept: $$0 = 2x - 3$$ $$2x = 3$$ $$x = \frac{3}{2} = 1.5$$ The x-intercept is positive, so the line crosses the x-axis to the right of the y-axis. 7. **Match with options:** - Positive slope: options A and B - Y-intercept below zero: option B - X-intercept to the right of y-axis: option B 8. **Conclusion:** The correct graph is option B. **Final answer:** Option B represents $$y = 2x - 3$$.