Final answer:
To find the equation of a line in slope-intercept form that is parallel to a given line and passes through a given point, we use the point-slope form. First, we rearrange the given equation into slope-intercept form to find the slope and y-intercept. Then, we use the point-slope form with the slope and the given point to find the equation of the line. The equation of the line parallel to y + 4 = 7(x - 12) that passes through (-3, 0) is y = 7x + 21, which is option b.
Step-by-step explanation:
The equation of the line parallel to y + 4 = 7(x - 12) and passing through the point (-3, 0) can be found by first writing the given equation in slope-intercept form to find the slope. The original equation simplifies to y = 7x - 88, so the slope is 7. Since parallel lines have the same slope, the parallel line will also have a slope of 7. To find the y-intercept of the new line, we can use the point (-3, 0) and the slope (7) in the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point (-3, 0) and m is the slope 7. Plugging in these values, we get y - 0 = 7(x - (-3)), y = 7x + 21. Therefore, the equation in slope-intercept form is y = 7x + 21, which corresponds to option b.