Find the equation of the line that is parallel...? Algebra 1, please help!Find the equation of the line that goes through the point (2,3) that is parallel to y = x + 1.
The point (2,3) verifies the equation provided y=x+1. That means that the required equation for the parallel line is the same equation, because parallel lines does not intersect.
To verify that we will have the same equation for both parallel lines, let us obtain the equation for the parallel line based on the data provided.
The equation for the line is:
y-y1=m(x-x1) where (x1,y1) any point on the line and m is the slope:
We have the point: (2,3)
Now substitute with the equation:
Since the line parallel to the line y=x+1 , then they have the same slope which is m=1 (x factor)
Add 3 to both sides:
y=x+1 which is the same line y=x+1
The given equation of the line is y = x+1
An equation of any line parallel to this is of the form where coefficient of x and y remains same but only constant term is set at k, an unknown , which would be detrmined fro the fact that the line passes through the point (2,3). So,
y = x+k is line ans as this passes through (2,3) , put x=2 and y= 3 in y = x+k and we get:
3 =2+k. Or k = 3-2 =1. So by resubstituting k=1 in the assume equation we get:
y = x+1. So we got the same given equation. That means the given point (2,3) is on the given line itself.