Need Help Point Slope Form and Slope Intercept form

Question

Question Determine an equation of the parallel line
described. Write your answer in both
point-slope form and slope-intercept form.

 

14. What is the equation of a line parallel to 

y = 4/5x + 2 that passes through (1,2)

Answer 1

First things first.  If we are asked to find a parallel line, that means we have a line with the same slope and different y-intercept.  Therefore the slope of our parallel line is 4/5.

 

Now plug this and the point (1,2) into the standard slope-intercept form of the equation of a line, y = m*x + b.  This looks like 2 = (4/5)*1 + b.  Solve for b and you get 6/5.  Therefore the slope-intercept equation of the parallel line is y = (4/5)*x + 6/5.

 

Now lets rewrite it in point-slope form.  Point-slope form of the line equation is y - b = m*x, therefore the parallel line written in point-slope form is y - 6/5 = (4/5)*x