Question

Which line is perpendicular to the line y=-1/3x-2 and passes through point (1,4)

Answer 1

Answer:

Option 3)  y = 3x+1

Step-by-step explanation:

Given equation is:

y = $-\frac{1}{3} x -2$

Perpendicular => It will have a slope of negative reciprocal to this slope

So the  ⊥ line has a slope = m =  3

Now,

Point = (x,y) = (1,4)

So, x = 1, y = 4

Putting this in slope intercept form to get b

=> $y = mx+b$

=> 4 = (3)(1) + b

=> b = 4-3

=> b = 1

Now, Putting m and b in the slope intercept form to get the required equation:

=> y = 3x+1

Answer 2

Answer:

y=3x+1

Option C is the correct option.

Given that,

$y = - \frac{1}{3} x - 2$

Which is in the standard form

$y = mx + c$

where, m= slope

c=y- intercept

$m1 = - \frac{1}{3}$

Slope of perpendicular lines is the product of slope is -1.

$m1.m2 = - 1 \\ - \frac{1}{3} \times m2 = - 1 \\ m2 = \frac{ - 1}{ \frac{ - 1}{3} } \\ m2 = 3$

Then, y=3x+c------> equation (i)

(X,y)=(1,4) ---- given

c=4-3x

c=4-3(1)

c=4-3

c=1

Put this in equation (i) we get,

y=3x+1

This is the required equation of the line.

Hope this helps...

Good luck on your assignment..