Question

Identify an equation in slope-intercept form for the line parallel toy = 5x + 2 that passes through (–6, –1).

Answer 1

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We know that if 2 lines are parallel to one another, their slopes are exactly the same. So the slope of the new line is 5, just like the slope of the original line.  We also have a coordinate in the form of (x, y) to fit into that line equation and solve it for b.  Like this: -1 = 5(-6) + b and -1 = -30 + b and b = 29. Now we can rewrite the equation fitting in the given slope and the newly found y-intercept value of 29: y = 5x + 29 is the new line.