Question

Find the equation of the line that is perpendicular to the line y = 4 and passes through the point (-2, 1).

Answer 1

Answer:

x = - 2

Step-by-step explanation:

y = 4 is the equation of a horizontal line parallel to the x- axis.

Thus a perpendicular line will be vertical and parallel to the y- axis.

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (- 2, 1) with x- coordinate - 2, thus

x = - 2 ← equation of perpendicular line

Answer 2

Answer:

We can see that the equation y=x%2B4 has a slope m=1 and a y-intercept b=4.

Now to find the slope of the perpendicular line, simply flip the slope m=1 to get m=1%2F1. Now change the sign to get m=-1. So the perpendicular slope is m=-1.

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1 and the coordinates of the given point .

y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula

y--1=-1%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=-1

y%2B1=-1%28x-0%29 Rewrite y--1 as y%2B1

 

y%2B1=-x-1%28-0%29 Distribute

y%2B1=-x%2B0 Multiply

y=-x%2B0-1 Subtract 1 from both sides.

y=-x-1 Combine like terms.

So the equation of the line perpendicular to y=x%2B4 that goes through the point  is y=-x-1.

Graph of the original equation y=x%2B4 (red) and the perpendicular line y=-x-1 (green) through the point .

3x-x+2=4

Step-by-step explanation: