Use the geometric interpretation of slope (rise divided by run) to find the slope of the line. Then, by identifying the y-intercept from the graph, write the slope-intercept form of the equation of the line.
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Part 1
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-16
-12
-8
-4
4
8
12
16
20
-20
-16
-12
-8
-4
4
8
12
16
20
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y
To find the slope of the line, we need to find the rise (change in y) divided by the run (change in x). Looking at the graph, we can see that the line passes through the points (0, 4) and (4, 12).
The rise is the change in y-coordinates: 12 - 4 = 8
The run is the change in x-coordinates: 4 - 0 = 4.
Therefore, the slope of the line is the rise divided by the run: 8/4 = 2.
To find the y-intercept, we can look at the point where the line intersects the y-axis. From the graph, it appears that the line intersects the y-axis at the point (0, 4).
Now we can write the slope-intercept form of the equation of the line, which is y = mx + b.
Since the slope is 2 and the y-intercept is 4, the equation is: y = 2x + 4.
To find the slope of the line using the geometric interpretation, we need to choose two points on the line and calculate the rise (change in y-coordinates) divided by the run (change in x-coordinates).
Let's choose the points (4, -8) and (-4, 12) from the graph.
Rise = Change in y-coordinates = 12 - (-8) = 20
Run = Change in x-coordinates = -4 - 4 = -8
Slope = Riserun = 20/-8 = -2.5
Therefore, the slope of the line is -2.5.
To write the slope-intercept form of the equation of the line, we need to use the slope and the y-intercept.
From the graph, we can identify the y-intercept as the point (0, -4).
The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values, we get:
y = -2.5x - 4
Therefore, the slope-intercept form of the equation of the line is y = -2.5x - 4.
To find the slope of the line using the geometric interpretation, you need to identify two points on the line. Let's choose two points from the graph, say (-4, -8) and (4, 8).
Now, we can calculate the rise and run. Rise is the vertical change between the two points and run is the horizontal change.
Rise = change in y-coordinates = 8 - (-8) = 16
Run = change in x-coordinates = 4 - (-4) = 8
Therefore, the slope is calculated as rise divided by run:
Slope = rise / run = 16 / 8 = 2
So the slope of the line is 2.
To write the slope-intercept form of the equation of the line, we need the slope and the y-intercept. Looking at the graph, the y-intercept is the point where the line intersects the y-axis. In this case, it appears to be the point (0, 0).
Now that we have the slope and the y-intercept, we can write the equation in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Substituting in the values, the equation becomes:
y = 2x + 0
Simplifying further, we get:
y = 2x
Therefore, the slope-intercept form of the equation of the line is y = 2x.