Find an equation for the line parallel to

Question

y=3x-7 with y-intercept (0,2).  Write the answer in slope-intercept form.

Answer 1

Consider:  What is the slope of the line y = 3x - 7?

 

This equation is already in slope-intercept form, so it's a simple matter to read it from the equation:  the coefficient of x is 3, so the slope is 3.  Any line parallel to this will also have a slope of 3.  Hence, in slope-intercept form, any parallel line will look like y = 3x + b, with b being the y-intercept.

 

What's the y-intercept in this specific case?  Conveniently, they tell you that it's 2.  So you just have to plug that in for b to get the equation of the line you're looking for:  y = 3x + 2.