Slope-Intercept Equation of the Line
Given a line, we can express it in the form:
y = mx + b
Where m is the slope and b is the y-intercept.
We are given the equation of a line:
2y = 2x + 4
Dividing by 2:
y = x + 2
Comparing with the generic equation in slope-intercept form, we can see that m = 1 and b=2.
Now we have to find the equation of a line that is parallel to that line and passing through the given point.
Parallel lines have the same value of the slope. Thus, the slope of our required line is m'=1
The equation of the line is so far:
y = x + b'
We need to find the value of b'. Here comes handy the use of the point (-5,-1). Substituting in the equation:
-1 = -5 + b'
Solving for b':
b' = -1 + 5 = 4
Now we have the complete equation of the line as required:
y = x + 4