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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Answer 1

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.