Question

Write the slope-intercept equation of the line parallel to 5y = 2x + 20 that goes through (-1, 3).

Answer 1

The first thing I'll do is solve "5y = 2x + 20" for "y=", so that I can find my reference slope:

y = (2/5)x + 4;

So the reference slope from the reference line is m = 2/5;.

Now I need to find two new slopes, and use them with the point they've given me; namely, with the point (-1, 3). They want me to find the line through (4, –1) that is parallel to 5y = 2x + 20; that is, through the given point, they want me to find a line that has the same slope as the reference line. 

Since a parallel line has an identical slope, then the parallel line through (-1, 3) will have slope m = 2/5. Now I have a point and a slope! So I'll use the point-slope form to find the line: y - 3 = (2/5)( x + 1);

Finally, y = (2/5)x + 17/5;