The general equation of a line is given as
[tex]\begin{gathered} y=mx+c \\ \text{where} \\ m=\text{slope / gradient} \\ c=\text{intercept on the y axis} \end{gathered}[/tex]Two lines are said to be parallel when they have the same slope or gradient that is
[tex]\begin{gathered} m_1=m_2 \\ m_{1=\text{slope of the first line}} \\ m_{2=\text{slope of the second line}} \end{gathered}[/tex]The equation of the line given is
[tex]y=-\frac{5}{2}x-7[/tex]By comparing coefficients,
[tex]m_1=-\frac{5}{2}[/tex]So from the options, we will figures out the equation that has the same gradient as -5/2
[tex]\begin{gathered} 5x-2y=8 \\ -2y=-5x+8 \\ \text{divide all through bu -2} \\ -\frac{2y}{-2}=-\frac{5x}{-2}+\frac{8}{-2} \\ y=\frac{5}{2}x-4 \end{gathered}[/tex]The slope above is 5/2 therefore the option A is not parallel to the line
[tex]\begin{gathered} 2x-5y=30 \\ -5y=-2x+30 \\ -\frac{5y}{-5}=-\frac{2x}{-5}+\frac{30}{-5} \\ y=\frac{2}{5}x-6 \end{gathered}[/tex]The slope above is 2/5 therefore Option B is not parallel to the line also
[tex]\begin{gathered} 2x+5y=-5 \\ 5y=-2x-5 \\ \frac{5y}{5}=-\frac{2x}{5}-\frac{5}{5} \\ y=-\frac{2}{5}x-1 \end{gathered}[/tex]The slope above is -2/5 Therefore Option C is also not parallel to the line
[tex]\begin{gathered} 5x+2y=4 \\ 2y=-5x+4 \\ \frac{2y}{2}=-\frac{5x}{2}+\frac{4}{2} \\ y=-\frac{5}{2}x+2 \end{gathered}[/tex]The slope above is -5/2 which is the same as the slope in the question
Therefore,
The correct answer is OPTION D
