Graph these equations: \( \begin{array}{l}x-y=6 \\ y=-2 x-3 \\ \text { (1) Click to select points on the aranh }\end{array} \)

Here’s how to graph the two equations step by step. 1. Rewrite the equations if needed so they’re in slope‐intercept form (y = mx + b):   • Equation 1: x – y = 6     Solve for y:      x – 6 = y  or y = x – 6   • Equation 2: y = –2x – 3     (It is already in the form y = mx + b) 2. Identify key points for each line:   a. For y = x – 6 (Line 1):     • y-intercept: Set x = 0 → y = 0 – 6 = –6. So point (0, –6).     • x-intercept: Set y = 0 → 0 = x – 6, so x = 6. So point (6, 0).     • You can also pick another point. For example, if x = 2 then y = 2 – 6 = –4 giving (2, –4).   b. For y = –2x – 3 (Line 2):     • y-intercept: Set x = 0 → y = –3. So point (0, –3).     • x-intercept: Set y = 0 → 0 = –2x – 3, solving gives –2x = 3 so x = –3/2 or (–1.5, 0).     • Pick another point: If x = 1 then y = –2(1) – 3 = –5 yielding (1, –5). 3. Plot the points on a coordinate plane:   • For y = x – 6, plot (0, –6) and (6, 0) and draw a straight line through them.   • For y = –2x – 3, plot (0, –3) and (–1.5, 0) (or (1, –5) and (0, –3)) and draw its line. 4. Find the intersection point (optional, but useful):   Since both equations represent lines, their intersection satisfies:    x – 6 = –2x – 3    Add 2x to both sides: 3x – 6 = –3    Add 6 to both sides: 3x = 3    Divide: x = 1    Plug x = 1 into equation y = x – 6: y = 1 – 6 = –5    Thus, the two lines intersect at (1, –5). 5. Final Graph:   • Draw the first line (y = x – 6) going through (0, –6) and (6, 0).   • Draw the second line (y = –2x – 3) going through (0, –3) and (–1.5, 0) (or through (1, –5) and (0, –3)).   • Mark the intersection point (1, –5) where the two lines cross. Below is a rough sketch of the graph layout: y ↑ | / | / ← y = x – 6 0 |--------•--------→ x | (6,0) | -3 | • (0,-3) | \ | \ -5 | • (1,-5) intersection | \ -6 | • (0,-6)\ | \ ------------------------------- Note: The above sketch provides an approximate visualization. In an interactive graphing tool, click on your chosen key points to precisely see the plotted lines. By following these steps, you’ve successfully graphed both equations and determined their point of intersection.