Question

question 1 pts
the graph of which equation is parallel to the graph of 2x - y = -1?
a 2x + y = 8
b y = -\frac{1}{2}x + 3
c y - 1 = 2(x - 3)
d y = -2x - 1
question 1 pts
cassidy’s family is driving home from vacation at an average speed of 55 mph. after 2 hours, they are 110 miles from home. what is an equation, in point - slope form, that represents their distance y, after x hours?
a. y - 110 = -55(x - 2)
b. y - 55 = 110(x - 2)
c. y - 2 = 55(x - 110)
d. y + 110 = -55(x + 2)

Explanation:

First Question (Parallel Lines)

Step1: Find slope of given line

Rewrite \(2x - y=-17\) in slope - intercept form (\(y = mx + b\), where \(m\) is slope).
\(y=2x + 17\), so slope \(m = 2\).

Step2: Find slopes of options

• Option A: \(2x + y=8\Rightarrow y=-2x + 8\), slope \(m=-2\).
• Option B: \(y =-\frac{1}{2}x+3\), slope \(m =-\frac{1}{2}\).
• Option C: \(y - 1=2(x - 3)\Rightarrow y=2x-6 + 1=2x-5\), slope \(m = 2\).
• Option D: \(y=-2x-1\), slope \(m=-2\).

Parallel lines have equal slopes. So the line with slope 2 is parallel.

Step1: Understand point - slope formula

Point - slope form is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point and \(m\) is slope.

Step2: Determine slope and point

• Speed is 55 mph, but since they are driving home, the distance from home is decreasing, so slope \(m=- 55\).
• After \(x = 2\) hours, \(y = 110\) miles from home, so the point is \((2,110)\).

Step3: Substitute into point - slope form

Substitute \(x_1 = 2\), \(y_1=110\), \(m=-55\) into \(y - y_1=m(x - x_1)\):
\(y - 110=-55(x - 2)\)

Answer:

C. \(y - 1=2(x - 3)\)

Second Question (Point - Slope Form)