1. **Problem Statement:** You need to create an image on a coordinate grid using at least 30 lines with specific requirements: 10 lines in point-slope form, 10 in standard form, 10 in slope-intercept form, 2 sets of parallel lines, 2 sets of perpendicular lines, at least 1 vertical and 1 horizontal line, and domain and range for each segment. 2. **Formulas and Important Rules:** - Point-slope form: $$y - y_1 = m(x - x_1)$$ where $m$ is slope and $(x_1,y_1)$ is a point on the line. - Standard form: $$Ax + By = C$$ where $A$, $B$, and $C$ are constants. - Slope-intercept form: $$y = mx + b$$ where $m$ is slope and $b$ is y-intercept. - Parallel lines have equal slopes. - Perpendicular lines have slopes that are negative reciprocals: if one slope is $m$, the other is $$-\frac{1}{m}$$. - Vertical lines have undefined slope and equation $$x = k$$. - Horizontal lines have zero slope and equation $$y = c$$. 3. **Example Lines:** - Point-slope: $$y - 2 = 3(x - 1)$$ - Standard: $$2x + 3y = 6$$ - Slope-intercept: $$y = -\frac{1}{2}x + 4$$ 4. **Parallel and Perpendicular Sets:** - Parallel set 1 (Orange): slopes 2, equations like $$y = 2x + 1$$ and $$y = 2x - 3$$. - Parallel set 2 (Green): slopes -1, equations like $$y = -x + 5$$ and $$y = -x - 2$$. - Perpendicular set 1 (Teal): slopes 3 and $$-\frac{1}{3}$$, e.g., $$y = 3x + 1$$ and $$y = -\frac{1}{3}x + 4$$. - Perpendicular set 2 (Yellow): slopes 0.5 and -2, e.g., $$y = 0.5x - 1$$ and $$y = -2x + 3$$. 5. **Vertical and Horizontal Lines:** - Vertical: $$x = 4$$ - Horizontal: $$y = -2$$ 6. **Domain and Range:** For each line segment, specify the $x$-values (domain) and $y$-values (range) visible on your graph paper. 7. **Summary:** Use these forms and rules to plot your lines, color code parallel and perpendicular sets as per the key, and label domain and range for each segment. This will create a neat, colorful coordinate grid image meeting all project requirements.