SOLUTION: What is the equation of a line that is parallel to the line {{{y=(3/4)x+2}}} and passes through the point (-2, 8)?

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Question 447233: What is the equation of a line that is parallel to the line and passes through the point (-2, 8)?
Found 2 solutions by solver91311, Leaf W.:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

There is a problem with the way you asked your question. You cannot find "the" equation of a line. The set of equations which graph to a given line is infinite, hence the best anyone can do is to derive an equation that is represented by a graph that is parallel to a line whose graph is a given equation and which passes through a given point.

In your case, the given equation is in slope-intercept form, namely , so that the slope of the line represented by the given equation can be determined simply by inspection of the coefficient on the term.

Parallel lines have identical slopes, hence an equation of a line parallel to the line represented by your original equation will have an identical coefficent on the term.

Use the point-slope form of an equation of a line:

where are the coordinates of the given point and is the determined slope.

John

My calculator said it, I believe it, that settles it

Answer by Leaf W.(135) (Show Source):
You can put this solution on YOUR website!
The equation is in y = mx + b form where m is the slope and b is the y-intercept. In this case, the slope is . Parallel lines have the same slope; therefore, the equation has a slope of . Then, use point-slope form, which is used to find the the equation of a line if you know its slope and one of its points. Point-slope form follows the equation , where is the y-coordinate of the point you know, m is the slope, and is the x-coordinate of the point you know.
==> You know that m = , is -2, and is 8.
==>
==>
==> Simplify:
==> Distribute into the x and 2:
==> Add 8 to both sides:
==> Find the least common denominator between 3/2 and 8:
==> Add 3/2 and 16/2:
***Therefore, the equation of the line is