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ANSWER
[tex]y\text{ = }\frac{4}{3}x\text{ - 13}[/tex]EXPLANATION
We want to write the equation of the line that goes through (6, -5) and is parallel to the line:
[tex]y\text{ = }\frac{4}{3}x\text{ + 5}[/tex]A line parallel to another line has the same slope as that line.
The slope of the given line is 4/3, so the slope of the line we are looking for is 4/3.
We now use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
where m = slope
(x1, y1) = point that the line passes through
Therefore, we have that:
[tex]\begin{gathered} y\text{ - (-5) = }\frac{4}{3}(x\text{ - 6)} \\ y\text{ + 5 = }\frac{4}{3}x\text{ - (}\frac{4}{3}\cdot6) \\ y\text{ + 5 = }\frac{4}{3}x\text{ - 8} \\ \Rightarrow\text{ y = }\frac{4}{3}x\text{ - 8 - 5} \\ y\text{ = }\frac{4}{3}x\text{ - 13} \end{gathered}[/tex]That is the equation of the line.
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