find an equation of the line that passes through (3,6) and is perpendicular to y=3x-4. Write in slope intercept form

Question

Please help me out with my math question above.

Answer 1

a line that is perpendicular to the line with equation y = 3x - 4 has a slope that is the negative reciprocal of the slope of the given line.

 

The general slope-intercept equation of a line is y = mx + b where m represents the slope.

 

So the slope of the given line is 3. Therefore the slope of the perpendicular line must be -1/3.

 

BTW, the reciprocal of 3, also written as 3/1 is 1/3.

 

So far our equation is y = (-1/3)x + b

 

If a line passes through a point, then the coordinates of that point must satisfy the equation of the line which you can plug in the values for x and y and get a true answer.

 

Let's do that.

 

6 = (-1/3)(3) + b

 

6 = -1 + b

 

7 = b

 

Now we found that b must be 7

 

So the complete equation of the line is y = (-1/3)x + 7

 

There is also the standard form of the equation of a line that looks like this: Ax + By = C

 

Starting with the slope-intercept form, we multiply both sides by 3 and then rearrange the terms to look like the standard form.

 

y = (-1/3)x + 7

 

3y = -x + 21

 

x + 3y = 7