Answer: y = (2/3)x + 2
Step-by-step explanation: We have a line that passes trough the points (0, -1) and (3, 1)
The slope of this line that passes trough the points (x1,y1) and (x2,y2) is:
s = (y2 - y1)/(x2 - x1)
s = ( 1 - (-1))/(3 - 0) = 2/3
So we know that this line has the shape:
Y1(x) = 2/3x + b
where b is the y intercept.
In order to find the value of b, we can do:
Y1(0) = -1 = (2/3)*0 + b = b
so we have that b = -1, and the equation of the line is:
y1(x) = (2/3)*x - 1
Now, we want to find another parallel line that passes through the point (-3,0)
because this new line is parallel to the one we previous had, their slopes must be equal, then the equation of our new line is:
Y2(x)= (2/3)x + c
and we need to find the value of c.
Y2(-3) = 0 = (2/3)*-3 + c = -2 + c = 0
c = 2
then the equation is:
Y2(x) = (2/3)x + 2
