Step 1
Given; What is the equation of the line that passes through (-4, 5) and is
parallel to the line 4x + 2y = 10?
Step 2
Parallel lines have the same slope. The slope of the given line is;
[tex]\begin{gathered} 4x+2y=10 \\ 2y=10-4x \\ y=\frac{10-4x}{2} \\ y=5-2x \\ slope=-2 \end{gathered}[/tex]
Thus the slope of the required line=-2
Step 3
The standard equation of a line is;
[tex]\begin{gathered} y=mx+b \\ m=-2=slope \\ b=y-intercept \\ y=-2x+b \\ y=5 \\ x=-4 \end{gathered}[/tex]
The y-intercept will be;
[tex]\begin{gathered} 5=-2(-4)+b \\ b=5-8=-3 \end{gathered}[/tex]
The answer will be; Option D
[tex]y=-2x-3[/tex]
