Final answer:
To find another point on a line with a slope of -3/4 that contains the point (4, -15), use the point-slope equation. By choosing x = 8 and plugging it into the equation, the point (8, -18) is determined to lie on the same line.
Step-by-step explanation:
If a line contains the point (4, -15) and has a slope of -3/4, to find other points on the line, you can use the point-slope form of a line equation, which is y - y1 = m(x - x1). Here, m is the slope and (x1, y1) is the given point. Therefore, we plug in our values to get y + 15 = -3/4(x - 4). If we want to find a specific point, we could choose a value for x and solve for y. Let's choose x = 8, then plug it into the equation: y + 15 = -3/4(8 - 4). This simplifies to y + 15 = -3, and then we isolate y to get y = -18. So, the point (8, -18) falls on the same line as (4, -15) with a slope of -3/4.
It's important to note that the slope of a line remains constant. Therefore, any point that lies on this line can be found using the same slope and the point-slope form equation. This is a key concept in the algebra of straight lines, relating to how the slope affects the rise and run between any two points on a straight line.