Question

A line is parallel to y = -2x + 1 and

intersects the point (4, 1). What is the
equation of this parallel line?
y = [?]x + [ ]

Answer 1

To begin to answer your question one has to first establish the criterion for the parallel lines.

Explanation:

To do that one has to realize that a parallel line has the same slope, and different y-intercept, and this can be realized in the following equation:

`y=x\\y=x+1`

As you can see those lines are parallel.

So to begin to answer your question we must recognize that the slope of the first function is the same as the other one:

`m_1=m_2=-2`

We can use then slope-intercept form to finish off the question:

`y=-2x+b\\y=1,x=4\\(1)=-2(4)+b\\9=b\\y=-2x+9`

Here is a picture of both the graphs plotted together: