Plz help which equation represents a line that is perpendicular to the line on the graph?
A) y=-4x+3
B) y= -1/4x+1
C) y=-1/x-2
D) y= 4x+4

Explanation:

The given visual line has a slope of -1/4. We can see this by starting at (0,2) and we do two things

a) move down 1

b) move over to the right 4

This leads to slope = rise/run = -1/4

Once we find the slope of the original line, we take the opposite reciprocal. This is also called the negative reciprocal. So we'll take the reciprocal of -1/4 to get -4/1 or just -4. Then we flip from negative to positive.

In short we flip the fraction and the sign. That has us go from -1/4 to 4.

The original slope is -1/4. The perpendicular slope is 4.

Side note: multiplying any two perpendicular slopes leads to -1. Neither line can be vertical.

So we found the slope of the perpendicular line to be m = 4.

We don't know which point the perpendicular line goes through, so theoretically we have infinitely many equations to pick from. They are all in the form y = 4x+b. Note how I replaced m in y = mx+b with 4.

So our answer will be in the form y = 4x+b. Choices A through C don't fit the description. Only choice D does. So choice D is the answer.

With y = 4x+4, the slope is 4 and the y intercept is 4.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

25/14 or 1.

step-by-step explanation:

the dots mean that it has infinitely more numbers behind it