Question

Y = 4x + 3

y = -1/4x - 5

What is the BEST description for the lines represented by the equations?
A) horizontal
B) intersecting
C) parallel
D) perpendicular

Answer 1

D) perpendicular!
A perpendicular's definition is: a straight line at an angle of 90° to a given line, plane, or surface.
And if you mark them on a graph you could see these two are opposite of each other.

Answer 2

Perpendicular.

D is the correct option.

Explanation:

The given equations are

`y=4x+4\\\\y=-(1)/(4)x-4`

The slope intercept form of a line is given by

`y=mx+b`

Here, m is the slope and b is the y intercept.

Comparing given equation with slope intercept form of the line

Slope of first line = 4

Slope of second line = -1/4

These two slopes are not equal hence, lines are not parallel.

We can see that -1/4 is the negative reciprocal of 4. Since.

`4\cdot-(1)/(4)=-1`

We know that the slopes of perpendicular lines are negative reciprocal of each other.

Hence, the lines are perpendicular.

D is the correct option.