Consider Line 1 with the equation: $y=-\frac{2}{3} x-18$
Give the equation of the line parallel to Line 1 which passes through $(-3,-7)$ :
Give the equation of the line perpendicular to Line 1 which passes through $(-3,-7)$ :

Step 1 ：Given the equation of Line 1: \(y=-\frac{2}{3} x-18\)

Step 2 ：We are asked to find the equation of a line parallel to Line 1 and a line perpendicular to Line 1, both passing through the point (-3,-7)

Step 3 ：The slope of a line parallel to a given line is the same as the slope of the given line. So, the slope of the line parallel to Line 1 is \(-\frac{2}{3}\)

Step 4 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line perpendicular to Line 1 is \(\frac{3}{2}\)

Step 5 ：We can use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), to find the equations of the lines. Here, \((x_1, y_1)\) is the point \((-3,-7)\), and \(m\) is the slope

Step 6 ：Substituting the values into the point-slope form, we get the equation of the line parallel to Line 1 as \(y=-\frac{2}{3}x-9\)

Step 7 ：Similarly, substituting the values into the point-slope form, we get the equation of the line perpendicular to Line 1 as \(y=\frac{3}{2}x-2.5\)

Step 8 ：\(\boxed{\text{Final Answer: The equation of the line parallel to Line 1 which passes through }(-3,-7)\text{ is }y=-\frac{2}{3}x-9\text{ and the equation of the line perpendicular to Line 1 which passes through }(-3,-7)\text{ is }y=\frac{3}{2}x-2.5}\)