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The points (−4, −3), (20, 15), and (48, 36) are points on the same line. identify another point on this same line.

1 Answer

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Final answer:

By calculating the slope between two provided points and using one of the points with the point-slope formula, we determined that the point (0, 0) lies on the same line as the given points.

Step-by-step explanation:

To identify another point on the same line as the points (-4, -3), (20, 15), and (48, 36), we need to determine the slope of the line and then use this slope to find a new point. The slope of a line passing through any two points, (x1, y1) and (x2, y2), is calculated using the formula (y2 - y1) / (x2 - x1). Let's use the points (-4, -3) and (20, 15) to find the slope (m).

m = (15 - (-3)) / (20 - (-4)) = 18 / 24 = 3 / 4

Now that we have the slope of the line, we can use one of the given points and the point-slope form of a line, y - y1 = m(x - x1), to write an equation for the line. Let's use point (20, 15).

y - 15 = (3 / 4)(x - 20)

This line equation allows us to compute y for any x we choose. Let's pick x = 0:
y - 15 = (3 / 4)(0 - 20)
y - 15 = -15
y = 0

Therefore, the point (0, 0) is another point that lies on this line.

User Michael Campbell
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