Question

How do you find an equation of the line having an x-intercept of 4 and parallel to \[2x+y=2\]?

Answer 1

Hint: In this problem, we have to find an equation of the line having an x-intercept of 4 and parallel to \[2x+y=2\]. We can see that this problem is based on slope and intercept. Here the x-intercept is given and the slope is hinted at by saying that the line is parallel to another line. We also know that parallel lines have the same slope. We can first find the slope of the parallel line then we can take the x-intercept where y is 0 to find the value of y-intercept to form an equation.

Complete step by step solution:
We know that the slope intercept form of the line is,
\[y=mx+c\] ……. (1)
Where, m is the slope and c is the y-intercept.
Here the x-intercept is given and the slope is hinted at by saying that the line is parallel to another line. We also know that parallel lines have the same slope
We know that the given parallel line equation is,
\[2x+y=2\]
We can write this equation as,
\[y=-2x+2\] …….. (2)
We can now compare the equation (1) and (2), we get
Slope, m = -2, y-intercept, c = 2.
We know that the x-intercept occurs when y = 0.
The given x-intercept = 4.
\[\begin{align}
  & \Rightarrow 0=-2\left( 4 \right)+c \\
 & \Rightarrow c=8 \\
\end{align}\]
Therefore, the slope is -2 and y-intercept of the new line is 8.
Therefore, the equation of line is \[y=-2x+8\].
Now we can plot the graph.

Note:
Students make mistakes while finding the slope of the required line. We should remember the slope of parallel lines are the same. We should also remember that, at x-intercept the value of y is 0 and at y-intercept the value of x is 0.