Question: Match each linear equation with its graph G K P B R Equation y = 5x + 3 y = \frac{1}{2} x + 3 y = -3x - 4 y = -3 y = -\frac{1}{4} x - 4 Graph Color a. purple (P) b. blue (B) c. green (G) d. red (R) e. black (K) top-left: green line G with positive slope, crossing the y-axis at 3. top-right: purple line P with steep positive slope, crossing the y-axis at 3. center: black line K with steep negative slope, crossing the y-axis at -4. bottom-left: blue line B with slight negative slope, crossing the y-axis at -4. bottom-right: red horizontal line R at y = -3.

1. **State the problem:** We need to match each linear equation with its corresponding graph based on slope and y-intercept. 2. **Recall the slope-intercept form:** The equation of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Analyze each equation:** - $y = 5x + 3$: slope $m=5$ (steep positive), y-intercept $3$ - $y = \frac{1}{2} x + 3$: slope $m=\frac{1}{2}$ (gentle positive), y-intercept $3$ - $y = -3x - 4$: slope $m=-3$ (steep negative), y-intercept $-4$ - $y = -3$: slope $m=0$ (horizontal line), y-intercept $-3$ - $y = -\frac{1}{4} x - 4$: slope $m=-\frac{1}{4}$ (gentle negative), y-intercept $-4$ 4. **Match with graph descriptions:** - Top-left green line G: positive slope, y-intercept $3$ → matches $y = \frac{1}{2} x + 3$ - Top-right purple line P: steep positive slope, y-intercept $3$ → matches $y = 5x + 3$ - Center black line K: steep negative slope, y-intercept $-4$ → matches $y = -3x - 4$ - Bottom-left blue line B: slight negative slope, y-intercept $-4$ → matches $y = -\frac{1}{4} x - 4$ - Bottom-right red line R: horizontal line at $y = -3$ → matches $y = -3$ 5. **Final matching:** - G: $y = \frac{1}{2} x + 3$ - P: $y = 5x + 3$ - K: $y = -3x - 4$ - B: $y = -\frac{1}{4} x - 4$ - R: $y = -3$