Through (-6,3) and parallel to 3x-9y=14

Question

linear functions and slope 

Answer 1

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Answer 2

Parallel lines have the same slope.  First, find the slope from the given line by putting it in slope-intercept form.

 

-9y = -3x + 14

 

y = (1/3)x - (14/9)

 

 

The slope is 1/3.

 

 

Now we use the point-slope form to find the parallel line going through the given points.

 

y - y₁ = m(x - x₁)

 

y - 3 = (1/3)(x + 6)

Answer 3

Must have same slope as 3x-9y=14

-9y = -3x +14

y = (1/3)x-14/9

 

Slope: m=1/3

 

 

Then y = mx+b ⇒ y = x/3 + b

 

To pass through (-6,3):

 

3 = (1/3)(-6) + b 

3 = -2 + b

b = 5

 

Final equation for the line:

 

y = x/3 + 5

Answer 4

Meera,

 

To find the equation of this line, you must first find the slope of the line 3x − 9y = 14 by rewriting it in slope-intercept form. This can be done by solving it for y in terms of x.

 

3x − 9y = 14

−9y = −3x + 14

y = (1/3)x − 14/9

 

The slope of the given line is 1/3. This will also be the slope of the line you seek.

 

Use the point-slope form to find it: y − y₁ = m(x − x₁):

 

y − 3 = (1/3)(x − (-6))

y − 3 = (1/3)(x + 6)

y − 3 = (1/3)x + 2

y = (1/3)x + 5

 

This will be the equation of the sought-after line. It can be rewritten in general form just as the line you were given, but I will leave this to you.