Final answer:
To find the equation of a line that is perpendicular to another line and passes through a given point, we can use the point-slope form of the equation. The equation of the line that passes through the point (-3, -8) and is perpendicular to the line y = -7 is y = 1/7x - 53/7.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line is y = -7, which is in the form y = mx + b, where m is the slope. In this case, the slope is -7. The negative reciprocal of -7 is 1/7.
Since the line we are looking for passes through the point (-3, -8), we can use the point-slope form of the equation: y - y1 = m(x - x1). Plugging in the values, the equation becomes y - (-8) = 1/7(x - (-3)). Simplifying, we can rewrite the equation as y + 8 = 1/7(x + 3). Further simplifying, we get y = 1/7x + 3/7 - 8. Combining the constants, the final equation is y = 1/7x - 53/7.