How To Find The Slope of a Line | Algebra

Summary

In this video, viewers learn how to calculate the slope of a line using two methods: the 'rise over run' approach and the formula m = (y2 - y1) / (x2 - x1). The video explains the concept of slope, demonstrating with examples using the y- and x-intercepts to calculate slope values. It also covers the special cases for horizontal and vertical lines, where the slope is always zero and undefined, respectively. The video emphasizes the simplicity of the 'rise over run' method for visual learners, ensuring viewers can confidently calculate slopes for various types of lines.

Takeaways

• 😀 The slope of a line is calculated by dividing the change in y (rise) by the change in x (run).
• 😀 The formula for slope is: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
• 😀 Using the rise over run method, the slope is found by determining how much the line moves vertically (rise) and horizontally (run).
• 😀 Example 1: For points (0, 2) and (-3, 0), the slope is 2/3, calculated by a rise of 2 and a run of 3.
• 😀 The formula method gives the same result: m = (2 - 0) / (0 - (-3)) = 2/3.
• 😀 The slope formula can be applied to any two points on a line, making it a versatile method for calculating slope.
• 😀 Negative slopes occur when the line moves downward as you move from left to right.
• 😀 Example 2: For points (-2, 4) and (2, 1), the slope is -3/4, with a rise of -3 and a run of 4.
• 😀 Horizontal lines always have a slope of 0 because the rise is 0, regardless of the run.
• 😀 Vertical lines always have an undefined slope because the run is 0, and division by zero is undefined.
• 😀 Both the rise over run and formula methods will give the same result, but the rise over run method may be simpler for visual learners.

Q & A

What is the formula used to calculate the slope of a line?

The formula to calculate the slope of a line is m = (change in y) / (change in x), or m = (y2 - y1) / (x2 - x1).

What do the terms 'rise' and 'run' represent when calculating the slope?

'Rise' represents the vertical change between two points on the line, while 'run' represents the horizontal change.

What are the coordinates of the y-intercept and the x-intercept in the example given?

The y-intercept is at (0, 2) and the x-intercept is at (-3, 0).

How do you calculate the slope using two points on a line?

To calculate the slope, subtract the y-values (y2 - y1) and the x-values (x2 - x1) of the two points. Then divide the difference in y by the difference in x.

What is the slope of a line where the rise is 2 and the run is 3?

The slope is 2/3, because the rise is 2 and the run is 3.

What is the slope of a horizontal line?

The slope of a horizontal line is always zero because the rise is zero, no vertical change occurs.

Why is the slope of a vertical line considered undefined?

The slope of a vertical line is undefined because the run is zero. Division by zero results in an undefined value.

How do you calculate the slope of a horizontal line using the formula?

When calculating the slope of a horizontal line, the y-values are always the same, so the difference in y (y2 - y1) is zero, resulting in a slope of zero.

What happens when you try to calculate the slope of a vertical line using the slope formula?

For a vertical line, the x-values are the same, so the difference in x (x2 - x1) is zero, and division by zero makes the slope undefined.

What is the difference between calculating the slope using the rise over run method versus the formula method?

The rise over run method visually identifies the change in y and x between two points, while the formula method uses the equation m = (y2 - y1) / (x2 - x1), which requires substituting the coordinates into the formula.