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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

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

step-by-step explanation: