- For inequality ① $y > -x - 5$: Graph the line $y = -x - 5$ with a dashed line (since it's a strict inequality). Shade the region above the line.
- For equation ② $y = -3x - 3$: Plot the y-intercept at $(0, -3)$. Use the slope $-3$ to find another point (e.g., move down 3, right 1 to $(1, -6)$). Draw a solid line through these points.
- For inequality ③ $x < -5$: Draw a vertical dashed line at $x = -5$. Shade the region to the left of the line.
- For equation ④ $x - 4y = 0$: Rewrite as $y = \frac{1}{4}x$. Plot the origin $(0, 0)$ and use the slope $\frac{1}{4}$ to find another point (e.g., $(4, 1)$). Draw a solid line through these points.
- For inequality ⑤ $5x - 3y \leq -15$: Rewrite in slope-intercept form: $y \geq \frac{5}{3}x + 5$. Graph the line $y = \frac{5}{3}x + 5$ with a solid line. Shade the region above the line.
- For equation ⑥ $y = 3x - 4$: Plot the y-intercept at $(0, -4)$. Use the slope $3$ to find another point (e.g., $(1, -1)$). Draw a solid line through these points.
Parent Tip: Review the logic above to help your child master the concept of graphing a linear equation worksheet.
