What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)? 3x − 4y = −17 3x − 4y = −20 4x + 3y = −2 4x + 3y = −6

Looking at the graph, we can read off the slope:  rise is -1 -3 = -4
and run is 3-(-3) = 6.  Thus, the slope is m = -4/6, or -2/3.

Two lines that are parallel have the same slope.  So the slope of the new line is also m = -2/3.

We are told that the new line passes through (-3,2).  Use the slope-intercept formula here:  y = mx + b

Subst. 2 for y and -3 for x, and -2/3 for m, 

2 = (-2/3)(-3) + b.  Find the y-intercept, b.

2 = 2 + b.  Then b = 0.  The equation of this new line parallel to the given line is y = mx + b,    or     y = (-2/3)x + 0     or    y = (-2/3)x