The slope of a line is –2 and its y-intercept is (0, 3). What is the equation of the line that is parallel to the first line and passes through (2, 2)?

Question

The slope of a line is –2 and its y-intercept is (0, 3). What is the equation of the line that is parallel to the first line and passes through (2, 2)?

Answer 1

If the second line is parallel to the first line, its slope must also be -2.  So it has an equation that looks like:

 

y = -2x + b

 

Since it passes through (2,2), you know that x = 2 and y = 2 satisfies the equation.  So:

 

2 = -2 * 2 + b

2 = -4 + b

6 = b

 

So the equation of the second line is y = -2x + 6