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Find the exact distance between the line 6x-y=-3 and the point (6,2). Show your work. Explain your answer.

Step-by-step explanation:

To find the distance between a point (m, n ) and the line

Ax + By + C = 0

d =

Here (m, n) = (6, 2) and rearranging the line

6x - y + 3 = 0 ← in general form

with A = 6, B = - 1 and C = 3 , then

d =

   =

   =  

Rationalise the denominator by multiplying numerator/ denominator by

= ×

= ← cancel 37 on numerator/ denominator

=

OR

≈ 6.08

Step-by-step explanation:

Turn the line given into slope-intercept form:

6x - y = -3

-y = -6x - 3

y = 6x + 3

We need to set this equal to the perpendicular version, and to do that we take the slope 6x and use the opposite reciprocal, and plug into the point-slope form:

y - 2 =

y =

6x + 3 =

x = 0

y = 0 + 3

y = 3

m=-16

step-by-step explanation:

using pemdas, (order of operations) you'll see the answer is 24.