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.
[tex]\begin{gathered} 5x-2y-4=0 \\ \Rightarrow2y=5x-4 \\ \Rightarrow y=\frac{5x}{2}-\frac{4}{2}=\frac{5x}{2}-2 \\ \Rightarrow y=\frac{5x}{2}-2 \\ \Rightarrow m=\frac{5}{2} \end{gathered}[/tex]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:
[tex]\begin{gathered} y-(-4)=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5x}{2}-5 \\ \Rightarrow y=\frac{5x}{2}-9 \\ \Rightarrow y+9=\frac{5}{2}x \\ \Rightarrow2y+18=5x \\ \Rightarrow5x-2y-18=0 \end{gathered}[/tex]The answer is 5x-2y-18=0
