Question

Write an equation of the line that passes through ( 6, 4 ) and is parallel to the line 3 y-x=-12

Answer 1

y = x/3 +2

Which can also be written as

y = (1/3)x +2

Explanation:

Now from the way your question is worded, I'll assume you mean 3y -x = -12, but do correct me.

3y -x = -12

3y = x -12

y = x/3 -12

So the gradient of this line is 1/3 and the y intercept is (0,-12).

We want a line parallel (with the same gradient) but a different y intercept.

If the line passes through (6,4) than the equasion of the line is equal when x = 6 and y = 4.

4 = 6/3 +c (c being the new y intercept for this parallel line)

4 = 2 +c

2 = c

Lets take that y intercept and put it back in our original equasion:

y = x/3 +2

And there's your answer :D

Answer 2

To find the equation of a line that is parallel to the line 3y - x = -12 and passes through the point (6, 4), we need to follow these steps:
Step 1: Determine the slope of the given line.
The equation of the given line is in the form y = mx + b, where m represents the slope. To find the slope, we need to rearrange the equation to isolate y.
Start by adding x to both sides: × + 3y = -12
Then subtract × from both sides: 3v = -x - 12
Finally, divide both sides by 3: y = (-1/3)x - 4
So, the slope of the given line is -1/3.
Step 2: Determine the slope of the parallel line.
Since the parallel line has the same slope as the given line, its slope is also -1/3.
Step 3: Use the point-slope form to write the equation.
The point-slope form of a linear equation is y - v1 = m(x - x1), where (x1, 1) is a point on the line and m is the slope.
Plugging in the values from the given point (6, 4) and the slope -1/3, we get:
y - 4 = (-1/3)(x - 6)
Step 4: Simplify the equation.
To simplify. distribute the -1/3 to the terms inside the parentheses:
y - 4 = (-1/3)x + 2
Now. add 4 to both sides to isolate v:
y = (-1/3)x + 6
Therefore, the equation of the line that passes through (6, 4) and is parallel to the line 3y - x = -12 is y = (-1/3)x + 6.