Answer:
y = 2x + 6
Explanation:
We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).
Parallel lines have the same slope, yet different y-intercepts.
So, we should first find the slope of y=2x+5.
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.
It is also the slope of the line parallel to it.
We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:
y = 2x + b
We need to find b.
As the equation passes through the point (-2, 2), we can use its values to help solve for b.
Substitute -2 as x and 2 as y.
2 = 2(-2) + b
Multiply.
2 = -4 + b
Add 4 to both sides.
6 = b
Substitute 6 as b.
y = 2x + 6