Question

Write the equation of the line that is parallel to the line y = 2x + 2 and passes through the point (5, 3)

Answer 1

y = 2x + 2 (The slope in y = mx + b is in the m position, therefore the slope of this line is 2)
Parallel lines have the same slope.

Now we have a choice on how to solve this....there are 2 ways.
(1) use y = mx + b (sub in all we know and solve for b)
slope(m) = 2
(5,3) x = 5 and y = 3
Now sub..
y = mx + b
3 = 2(5) + b
3 = 10 + b
3 - 10 = b
-7 = b
Therefore, the parallel line is : y = 2x - 7

(2) This can also be solved by using the point slope formula:
y - y1 = m(x - x1)
slope(m) = 2
(5,3) x1 = 5 and y1 = 3
now we sub..
y - y1 = m(x - x1)
y - 3 = 2(x - 5)
y - 3 = 2x - 10
y = 2x - 10 + 3
y = 2x - 7

either way, you will arrive at the correct answer.

Answer 2

thank you

Answer 3

no problem :) Do you have any questions ?