Chapter 4.3, Problem 50PFA

To determine

To Find: The equation of line which is parallel to $y=-2x+4$

Answer to Problem 50PFA

All the three lines $y+1=-2x+3,2x+y=5\&y=2\left(3-x\right)$ are parallel to $y=-2x+4$ option ‘D’ is correct.

Explanation of Solution

Given information:

The equation given line is $y=-2x+4$ and other three line is $y+1=-2x+3,2x+y=5\&y=2\left(3-x\right)$

Concept and Formula Used:

Slope intercept form of a line: $y=mx+c$

Parallel lines: If lines are parallel then the slopes of lines are equal

Calculation:

The given line is $y=-2x+4$

Now, find the slope of given line by comparing it with $y=mx+c$ .

The slope of line $y=-2x+4$ is $-2$ .

Now, find the slope of first line

  $\begin{array}{l}y+1=-2x+3\\ y=-2x+3-1\\ y=-2x+3\end{array}$

Comparing it with $y=mx+c$ the slope of line $y+1=-2x+3$ is $-2$

As slope of line $y+1=-2x+3$ is equal to slope of line $y=-2x+4$ therefore both the lines are parallel.

Now, find the slope of second line

  $\begin{array}{l}2x+y=5\\ y=-2x+5\end{array}$

Comparing it with $y=mx+c$ the slope of line $2x+y=5$ is $-2$

As slope of line $2x+y=5$ is equal to slope of line $y=-2x+4$ therefore both the lines are parallel.

Now, find the slope of third line

  $\begin{array}{l}y=2\left(3-x\right)\\ y=-2x+6\end{array}$

Comparing it with $y=mx+c$ the slope of line $y=2\left(3-x\right)$ is $-2$

As slope of line $y=2\left(3-x\right)$ is equal to slope of line $y=-2x+4$ therefore both the lines are parallel.

Therefore all the three lines $y+1=-2x+3,2x+y=5\&y=2\left(3-x\right)$ are parallel to $y=-2x+4$

Conclusion:

All the three lines $y+1=-2x+3,2x+y=5\&y=2\left(3-x\right)$ are parallel to $y=-2x+4$ option ‘D’ is correct.