write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (6,2) -2x+3y=19

Answer 1

For a line to be parallel to another line, they must have the same slope.

The slope of our existing line is...

-2x + 3y = 19

3y = 19+2x

y = 2/3x + 19/3

So our slope is 2/3 for both lines.

y = 2/3x + SOMETHING (k) and we know that (6,2) has to work for this new equation. Let's plug it in...

2 = 2/3 (6) + k

2 = 4 + k

k = -2

So our line should be y = 2/3x -2