Question

test - equations of || and ⊥ lines b name class tell if the two given lines are parallel, perpendicular, or just intersect. 1. -2x + y = -1 and -6x + 3y = 6 2. y = -\frac{3}{4}x + 12 and 3y = 4x - 9 circle the correct answer parallel perpendicular intersect circle the correct answer parallel perpendicular intersect 3. y = \frac{1}{2}x - 2 and 2x + y = -2 4. x - 3y = 3 and 2x - 3y = 6 circle the correct answer parallel perpendicular intersect circle the correct answer parallel perpendicular intersect use the slope formula to find the slope of the given line. m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} 5. \overleftrightarrow{ab} given a(3,-4) and b(-5,-2) 6. \overleftrightarrow{st} given s(6,2) and t(2,-4) m = m = 7. graph y = \frac{2}{3}x - 1 it is graphed already graph the line that is parallel to line in #7 the passes through (-1,2) graph the line that is perpendicular to e in #7 that passes through (3, -2)

Explanation:

Step1: Find the slope of line \(AB\)

Given \(A(3,-4)\) and \(B(-5,-2)\), use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here \(x_1 = 3,y_1=-4,x_2=-5,y_2 = -2\).
\(m=\frac{-2-(-4)}{-5 - 3}=\frac{-2 + 4}{-8}=\frac{2}{-8}=-\frac{1}{4}\)

Step2: Find the slope of line \(ST\)

Given \(S(6,2)\) and \(T(2,-4)\), use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here \(x_1 = 6,y_1=2,x_2=2,y_2=-4\).
\(m=\frac{-4 - 2}{2-6}=\frac{-6}{-4}=\frac{3}{2}\)

Answer:

1. \(m =-\frac{1}{4}\)
2. \(m=\frac{3}{2}\)