unit 3 lesson 5
slope as unit rate practice
use the image to answer the question
use similar triangles to determine the slope of the line. write your answer in fraction form.
(0,0), (2,1), (4,2), (6,3), (8,4)
the slope is _
To determine the slope using similar triangles, we can compare the change in the y-coordinate to the change in the x-coordinate.
Starting with point (0,0), we can see that as x increases by 2 units, y increases by 1 unit.
So, the slope between (0,0) and (2,1) is:
Change in y / Change in x = 1/2.
We can observe the same pattern for the other points:
(2,1) and (4,2) have a slope of 1/2,
(4,2) and (6,3) have a slope of 1/2,
(6,3) and (8,4) have a slope of 1/2.
Therefore, the slope of the line connecting these points is 1/2.
To determine the slope of the line using similar triangles, we can take any two points on the line and find the vertical change (rise) and horizontal change (run) between them.
Let's choose the points (0,0) and (2,1).
The vertical change (rise) between these two points is 1 unit (from 0 to 1), and the horizontal change (run) is 2 units (from 0 to 2).
Since slope is defined as rise over run, we can express the slope as a fraction:
slope = rise / run = 1/2
Therefore, the slope of the line is 1/2.
To determine the slope of the line using similar triangles, we need to calculate the ratio of the change in the y-coordinate to the change in the x-coordinate for any two points on the line.
Let's choose the points (0,0) and (2,1) to calculate the slope:
Change in y = 1 - 0 = 1
Change in x = 2 - 0 = 2
The slope is the ratio of the change in y to the change in x:
slope = (Change in y) / (Change in x)
slope = 1/2
Therefore, the slope of the line is 1/2.