A) ON SEPARATE GRAPHS ( THE CARTESIAN PLANE), DRAW THE FOLLOWING STRAIGHT LINES USING THE GIVEN DOMAINS. I) \( \mathrm{y}=\mathrm{x}+7 \) for \( \{x:-3 \leq x \leq 3\} \) II) \( 3 \mathrm{y}+6 \mathrm{x}=12 \) for \( \{x:-1 \leq x \leq 4\} \) III) \( \mathrm{y}=\mathrm{x} \) for \( \{x:-3 \leq x \leq 3\} \) IV) \( \mathrm{y}=5 \mathrm{x} \) for \( \{x:-2 \leq x \leq 2\} \)

To draw the given straight lines, start by plotting their respective points based on the provided equations and domains. For the first line \( \mathrm{y}=\mathrm{x}+7 \): 1. When \( x = -3 \), \( y = -3 + 7 = 4 \). 2. When \( x = 3 \), \( y = 3 + 7 = 10 \). Plot the points \((-3, 4)\) and \((3, 10)\), then connect them with a straight line. For the second line \( 3\mathrm{y}+6\mathrm{x}=12 \): 1. Rearranging gives \( \mathrm{y} = \frac{12 - 6\mathrm{x}}{3} \). 2. When \( x = -1 \), \( y = \frac{12 + 6}{3} = 6 \). 3. When \( x = 4 \), \( y = \frac{12 - 24}{3} = -4 \). Plot the points \((-1, 6)\) and \((4, -4)\), and draw the line through them. For the third line \( \mathrm{y}=\mathrm{x} \): 1. When \( x = -3 \), \( y = -3 \). 2. When \( x = 3 \), \( y = 3 \). Plot the points \((-3, -3)\) and \((3, 3)\), and connect them. For the fourth line \( \mathrm{y}=5\mathrm{x} \): 1. When \( x = -2 \), \( y = -10 \). 2. When \( x = 2 \), \( y = 10 \). Plot the points \((-2, -10)\) and \((2, 10)\), and draw the line. Now, enjoy the artistic exploration of graphing these relationships on the Cartesian plane!