Question

1. jamie was graphing the amount of money he pays for riding in a taxi. the price was $2 for every mile. he knew the equation to graph is y = 2x. which one of the following graphs shows the relation between the amount he needs to pay and the distance he rides? (y - axis is for money, x - axis is for miles) (g2b)

pick the right answer from the possible selections on your screen in eduphoria.
tell whether the lines through the given points are parallel, perpendicular, or neither for the questions 5 and 6. (g2b)

1. line 1: (1,2), (2,0)

line 2: (0, - 1), (-2,-2)
pick the right answer from the possible selections on your screen in eduphoria.

Explanation:

4.

Step1: Analyze the equation y = 2x

The equation y = 2x is a linear - function with a slope of 2 and a y - intercept of 0. This means the line passes through the origin (0,0) and for every 1 unit increase in x, y increases by 2 units.

Step2: Check each option

• Option A: The line does not pass through the origin.
• Option B: This is a set of discrete points, but the relationship y = 2x is a continuous linear function.
• Option C: The line passes through the origin (0,0) and has a positive slope of 2. This is the correct graph for y = 2x.
• Option D: This is a set of discrete points, and the relationship y = 2x is a continuous linear function.

Step1: Calculate the slope of Line 1

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Line 1 with points $(1,2)$ and $(2,0)$, $m_1=\frac{0 - 2}{2 - 1}=\frac{-2}{1}=-2$.

Step2: Calculate the slope of Line 2

For Line 2 with points $(0, - 1)$ and $(-2,-2)$, $m_2=\frac{-2+1}{-2 - 0}=\frac{-1}{-2}=\frac{1}{2}$.

Step3: Determine the relationship between the lines

Two lines are parallel if their slopes are equal, perpendicular if the product of their slopes is - 1, and neither if neither of these conditions is met. Since $m_1\times m_2=(-2)\times\frac{1}{2}=-1$, the two lines are perpendicular.

Answer:

C

5.