The equation of a line passing through (-1,-4) and perpendicular to y=3x-1

Question

The equation of a line passing through (-1,-4) and perpendicular to y=3x-1

Answer 1

If line a and b are perpendicular, the slope of line b is the negative reciprocal of the slope of line a. Negative reciprocal means you flip the fraction and add a negative sign. So the negative reciprocal of 4 is -1/4. 

 

In this case, your line is in the form y=mx+b. Your slope is m, or 3. Take the negative reciprocal of 3 to find the new line's slope. (b is the y-intercept, where x=0).

 

then you will have the m in y=mx+b. To find b, plug in -1 for x and -4 for y. Since the line passes through there, it must be a solution to the line's equation. You will have y, m, and x, so you just need to solve for b, the y-intercept. 

 

Then write it as y=mx+b with your slope as m and your y-intercept as b. 

Answer 2

The slope-intercept format for a line is expressed as:

y = mx + b

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

 

Therefore, the slope of the line y = 3x - 1 is equal to 3.

 

For perpendicular lines, the slopes are the negative inverse of each other. Therefore, the slope of the line perpendicular to this line would be -1/3.

 

The equation of the line would therefore be:

y = (-1/3)x + b

 

We can find the y-intercept "b" because we know the line passes thru (-1,-4). Therefore we know that x = -1 when  y=-4.

 

Plugging these values into the equation gives:

-4 = (-1/3)(-1) + b

Solving for b, we get

b = -4 - 1/3

b = -13/3

 

Therefore, the equation of the perpendicular line is:

y = (-1/3)x - 13/3 or

3y = -x -13

x + 3y + 13 = 0