Use similar triangles to determine the slope of the line.

Question

(3,9) (2,6) (1,3)(0,0)

Answer 1

Let's consider two points on the line: (3,9) and (0,0).

The slope of the line passing through these two points can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substitute the coordinates of the two points into the formula:

m = (9 - 0) / (3 - 0)
m = 9 / 3
m = 3

Therefore, the slope of the line passing through the points (3,9) and (0,0) is 3.

Next, let's consider two other points on the line: (2,6) and (1,3).

Using the same formula:

m = (6 - 3) / (2 - 1)
m = 3 / 1
m = 3

Therefore, the slope of the line passing through the points (2,6) and (1,3) is also 3.

Since the slope of the line passing through any two points on the line is 3, we can conclude that the slope of the line is 3.