Find the equation for the line passing through the point (-2, -4) and parallel to the line whose equation is y=2x+5

Parallel lines have the same slope. So we need to find the slope of the given line and then use that same slope for the new line that goes through the point (-2, -4). It looks like our line is already in the form y = mx + b where m is the value of the slope. Our line has a 2 in the place of m, so the slope of the given line is 2. That means that the slope of the new line is also 2. From this point you can use either point-slope form to write the equation of the new line or slope-intercept form to write the equation of the new line. Either way you'll get the same equation. Some of my students prefer to solve for b, while others prefer the point-slope, which is more direct. Using the point-slope form first:

y - (-4) = 2( x - (-2)) and

y + 4 = 2(x + 2) and

y + 4 = 2x + 4 so

y = 2x

Using the slope-intercept form:

-4 = 2(-2) + b and

-4 = -4 + b so

b = 0 and the equation is

y = 2x + 0 or simply,

y = 2x