Question

geometry name colt law date 11/20/2025 unit 4 part 2 test semester a please make sure that you show work for finding the slope of the line and the equation of the line. 1.) the equation of line a is y = 2x + 5. given line b that passes through points (2, 2) and (-2, -6). a) what is the slope of line a? b) what is the slope of line b? c) what is the equation of line b in slope - intercept form? d) are line a and b parallel, perpendicular, or neither?

Explanation:

Step1: Find slope of line a

The equation of line a is \(y = 2x+5\). In the slope - intercept form \(y = mx + b\) (where \(m\) is the slope), for line a, \(m = 2\).

Step2: Find slope of line b

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \((x_1,y_1)=(2,2)\) and \((x_2,y_2)=(-2,-6)\), \(m=\frac{-6 - 2}{-2 - 2}=\frac{-8}{-4}=2\).

Step3: Find equation of line b in slope - intercept form

We know \(m = 2\). Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((2,2)\):
\(y - 2=2(x - 2)\)
\(y-2 = 2x-4\)
\(y=2x - 2\)

Step4: Determine the relationship between line a and line b

Since the slope of line a (\(m_a = 2\)) and the slope of line b (\(m_b = 2\)) are equal (\(m_a=m_b\)), the lines are parallel.

Answer:

a) \(2\)
b) \(2\)
c) \(y = 2x-2\)
d) Parallel