Question

What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?
answer choices:

A. y=-4/3x+7

B. y=-3/4x+7

C. y=-3/4x+4

D. y=-4/3x+4

Answer 1

Answer:

Option A

y=-4/3x+7

Step-by-step explanation:

To solve this, we need to understand the various components of the equation of a straight line.

A straight line has the equation: y =mx + c

m is the slope and c is the intercept on the y-axis. If we can get these two components, we can figure out the equation for the new line.

Calculating the slope, m

To obtain the slope of the new line, we use the fact that it is perpendicular to the slope of the line y = 3/4x-2.

This means that

3/4 X m = -1

m = -4/3

To obtain the intercept, c

The intercept can be obtained by adding 3 to the y-component of (0, 4).

This will give (0, 7). Hence the intercept c will be 7.

Therefore, the equation of the line will be y = -4/3x+7. Option A