The equation of a line that is parallel to 3x=4y and has the same y-intercept as 2x-3y=6 is:
y = (3/4)*x - 2
How to get the equation of the line?
A general linear equation is written as:
y = a*x + b
Where b is the y-intercept and a is the slope.
Such that two lines are parallel if the lines have the same slope but different y-intercepts.
So, if we want to have a line parallel to:
3x = 4y
y = (3/4)*x
Then the slope must be 3/4.
And the line must have the same y-intercept than:
2x - 3y = 6.
We can rewrite that to get:
-3y = 6 - 2x
y = (6/-3) + (2/3)*x
y = (2/3)*x - 2
So this linear equation has a y-intercept equal to -2, then our linear equation is:
y = (3/4)*x - 2
If you want to learn more about linear equations:
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