Question

Find the equation of the line through (2,-4) and parallel to the line 5x-2y-4=0. Write your answer in general form.

Answer 1

We can find the equation of a line given one point and its slope.

Remember that two parallel lines have the same slope; therefore, the slope of 5x-2y-4=0 is equal to the slope of the line we are trying to find.

`\begin{gathered} 5x-2y-4=0 \\ \Rightarrow2y=5x-4 \\ \Rightarrow y=(5x)/(2)-(4)/(2)=(5x)/(2)-2 \\ \Rightarrow y=(5x)/(2)-2 \\ \Rightarrow m=(5)/(2) \end{gathered}`

Then, we have got everything we need, the slope is equal to 5/2 and a point in the line is (2,-4)

The equation is:

`\begin{gathered} y-(-4)=(5)/(2)(x-2) \\ \Rightarrow y+4=(5)/(2)(x-2) \\ \Rightarrow y+4=(5x)/(2)-5 \\ \Rightarrow y=(5x)/(2)-9 \\ \Rightarrow y+9=(5)/(2)x \\ \Rightarrow2y+18=5x \\ \Rightarrow5x-2y-18=0 \end{gathered}`

The answer is 5x-2y-18=0