-(3-6)-slope-intercept-form.jpeg "(2 4) (3 6) Slope Intercept Form")
Understanding Slope-Intercept Form: (2, 4) and (3, 6) Examples
Slope-intercept form is a fundamental concept in algebra and graphing, used to represent linear equations. In this article, we'll delve into the concept of slope-intercept form, using the examples of (2, 4) and (3, 6) to illustrate its application.
What is Slope-Intercept Form?
The slope-intercept form of a linear equation is written in the format:
y = mx + b
where:
- m represents the slope (a measure of how steep the line is)
- b represents the y-intercept (the point where the line crosses the y-axis)
- x and y are the coordinates of a point on the line
Example 1: (2, 4)
Let's consider the point (2, 4). To find the slope-intercept form of a line that passes through this point, we need to determine the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Since we only have one point, we can't use this formula directly. However, we can use the concept of slope to find the answer. Let's assume the slope is 2 (we'll see why later). Then, the equation becomes:
y = 2x + b
Step 2: Find the y-intercept (b)
Now that we have the slope, we can find the y-intercept by plugging in the point (2, 4) into the equation:
4 = 2(2) + b 4 = 4 + b b = 0
So, the slope-intercept form of the line that passes through (2, 4) is:
y = 2x + 0 y = 2x
Example 2: (3, 6)
Let's repeat the process for the point (3, 6).
Step 1: Find the slope (m)
Again, let's assume the slope is 2 (we'll see why later). Then, the equation becomes:
y = 2x + b
Step 2: Find the y-intercept (b)
Now that we have the slope, we can find the y-intercept by plugging in the point (3, 6) into the equation:
6 = 2(3) + b 6 = 6 + b b = 0
So, the slope-intercept form of the line that passes through (3, 6) is:
y = 2x + 0 y = 2x
Observations and Conclusion
From the two examples, we can observe that both lines have the same slope (m = 2) and y-intercept (b = 0). This means that the lines are identical, and both pass through the origin (0, 0).
In conclusion, the slope-intercept form is a powerful tool for representing linear equations. By understanding how to find the slope and y-intercept, we can write the equation of a line in slope-intercept form, making it easier to graph and analyze.
