If a line is parallel to another line, both lines have the same slope. The slope of the line is -4, which means the slope of the parallel line would be -4.
Parallel lines never intersect, which means the y-intercept of the parallel line cannot be 5. The y-intercept of the parallel line is when x = 0. You know that one of the points of the new, parallel line is (4,7). So what happens if you use the slope to find the y-intercept? So you can take the point (4,7) and subtract 4 from the x-coordinate and add 16 to the y-coordinate (Remember, this is the slope because the change in y is 16, and the change in x is -4, making the slope -4). When you do this, then you get that the y-intercept is 23. Therefore, the equation for the line is y = -4x + 23.
