Question

the line passes through the orgin and has a slope of 4. what is the equation of the line that is parallel to the first line and passes through the point (1,-2)

Answer 1

ur line has a slope of 4...a parallel line will have the same slope

y = mx + b
slope(m) = 4
(1,-2)...x = 1 and y = -2
now we sub...we r looking for b, the y intercept
-2 = 4(1) + b
-2 = 4 + b
-2 - 4 = b
-6 = b

so ur parallel line will be : y = 4x + (-6) or y = 4x - 6

Answer 2

An equation of the line has a form of:

y = mx + b

where m is the slope and b is the y-intercept. Parallel lines will have the same slope since they are lines that never meet however they have different y-intercepts. Therefore, the equation of the line parallel to the one that passed through the origin is:

y = 4x + b

Substitute the given points,

-2 = 4(1) + b
b = -6

y = 4x - 6