parallel lines and slope

Question

the line passes through (2,-6) and is parallel to the line whose equation is y=2x+3

Answer 1

One way to express the equation of a line is point slope form:

(y-y_o)=m(x-x_o)

m is the slope or 2 in this case due to its parallelism and y₀ and x_o are any coordinate on the line.

Thus, (y+6)=2(x-2)

 

In slope intercept form just simplify:

 

y+6=2x-4

y=2x-10

Answer 2

The line  y = 2x + b    is parallel to the line   y = 2x + 3    (because they have the same slope=2).  And it passes through the point (2,-6), so, putting those coordinates into the equation for the line, we can solve for b:

    -6 = 2(2) + b

       b = 10

 

Thus, y = 2x + 10