Question

Write the equation of the line that goes through the point (6,-5) and is parallel to the line y = (4/3)x + 5.

Answer 1

`y\text{ = }(4)/(3)x\text{ - 13}`

Step-by-step explanation

We want to write the equation of the line that goes through (6, -5) and is parallel to the line:

`y\text{ = }(4)/(3)x\text{ + 5}`

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:

`\begin{gathered} y\text{ - (-5) = }(4)/(3)(x\text{ - 6)} \\ y\text{ + 5 = }(4)/(3)x\text{ - (}(4)/(3)\cdot6) \\ y\text{ + 5 = }(4)/(3)x\text{ - 8} \\ \Rightarrow\text{ y = }(4)/(3)x\text{ - 8 - 5} \\ y\text{ = }(4)/(3)x\text{ - 13} \end{gathered}`

That is the equation of the line.