Question

Exit Ticket 1. **Line m is represented by the equation y = -x + 4 while line k is represented by the equation -2x + 4y = 16. Line m and line k are because (2 points) Blank #1 Blank #2 Blank #1: Blank #2: (A) (A) (B) (C) (D) (B) the same line parallel perpendicular neither parallel nor perpendicular their slopes are the same their slopes are opposite reciprocals their slopes are inverse reciprocals their slopes have no relationship (C) (D)

Answer 1

First of all, consider that the general for of an equation of a line is given by:

y = mx + b

where m is the slope of the line and b the y-intercept.

You have the following equations:

y = 2/3x + 4

-2x + 4y = 16

The first equation is already in the form y=mx+b, here, you can notice that the slope is m = 2/3

For the second equation, solve it for y, just as follow:

-2x + 4y = 16 add 2x both sides

4y = 2x + 16 divide by 4 both sides

y = 2/4 x + 16/4 simplify fractions

y = 1/2 x + 4

the slope of this line is m = 1/2

Take into account that parallel lines have the same slope and perpendicular lines are related as follow:

m1 = -1/m2

Then, you can conclude that the line are not parallel neither perpendicular.

Hence, the answer is:

Blank #1

D) neither parallel nor perpendicular

Blank#2

D) their slopes have no relationship