Question

3. What is the equation of the line that passes through (-4, 5) and isparallel to the line 4x + 2y = 10?Ax + 3y2x + 10x + 52.x=-3B.D.y'

Answer 1

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;

`\begin{gathered} 4x+2y=10 \\ 2y=10-4x \\ y=(10-4x)/(2) \\ y=5-2x \\ slope=-2 \end{gathered}`

Thus the slope of the required line=-2

Step 3

The standard equation of a line is;

`\begin{gathered} y=mx+b \\ m=-2=slope \\ b=y-intercept \\ y=-2x+b \\ y=5 \\ x=-4 \end{gathered}`

The y-intercept will be;

`\begin{gathered} 5=-2(-4)+b \\ b=5-8=-3 \end{gathered}`

The answer will be; Option D

`y=-2x-3`