Parallel lines have the exact same slope. In y = mx + b form, the line we were given is y = -4x+9, where -4 is the slope and 9 is the y intercept. If the "new" line passes through (0, 7), we have the x and y and slope we need to write this new equation. In y=mx+b, y is the y coordinate of the given point: 7, x is the x coordinate in the given point: 0. The slope, remember, is -4. We fill in accordingly and solve for b. 7 = -4(0)+b and b = 7. Filling that back in we will have a new equation y = -4x=7, parallel to the given line.
