Find The Slope Of The Line That Goes Through The Given Points: { (-2,2)$}$ And { (-5,8)$}$.Select The Correct Choice Below And, If Necessary, Fill In The Answer Box To Complete Your Answer.A. The Slope Is { \square$}$.

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Introduction

In mathematics, the slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. In this article, we will learn how to find the slope of a line given two points.

What is Slope?

The slope of a line is a numerical value that represents the rate of change of the line. It is denoted by the letter "m" and is calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Finding the Slope of a Line Given Two Points

To find the slope of a line given two points, we can use the formula above. Let's consider the two points (-2, 2) and (-5, 8). We can plug these values into the formula to find the slope.

Step 1: Identify the Coordinates of the Two Points

The coordinates of the two points are (-2, 2) and (-5, 8).

Step 2: Plug the Values into the Formula

m = (y2 - y1) / (x2 - x1) m = (8 - 2) / (-5 - (-2)) m = 6 / -3 m = -2

Step 3: Simplify the Fraction

The fraction -6/3 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

m = -6 / 3 m = -2

Conclusion

In this article, we learned how to find the slope of a line given two points. We used the formula m = (y2 - y1) / (x2 - x1) and plugged in the coordinates of the two points (-2, 2) and (-5, 8) to find the slope. The slope of the line is -2.

Example Problems

Problem 1

Find the slope of the line that goes through the points (3, 4) and (6, 8).

Solution

m = (8 - 4) / (6 - 3) m = 4 / 3

Problem 2

Find the slope of the line that goes through the points (-1, 2) and (2, 5).

Solution

m = (5 - 2) / (2 - (-1)) m = 3 / 3 m = 1

Tips and Tricks

  • When finding the slope of a line, make sure to use the correct formula: m = (y2 - y1) / (x2 - x1).
  • When plugging in the values into the formula, make sure to use the correct coordinates of the two points.
  • When simplifying the fraction, make sure to divide both the numerator and the denominator by their greatest common divisor.

Common Mistakes

  • Using the wrong formula to find the slope of a line.
  • Plugging in the wrong values into the formula.
  • Not simplifying the fraction correctly.

Real-World Applications

  • Finding the slope of a line is an important concept in mathematics and has many real-world applications, such as:
  • Calculating the rate of change of a quantity over time.
  • Determining the steepness of a hill or a roof.
  • Finding the equation of a line that passes through two points.

Conclusion

In conclusion, finding the slope of a line given two points is an important concept in mathematics. We learned how to use the formula m = (y2 - y1) / (x2 - x1) to find the slope of a line and applied it to two example problems. We also discussed common mistakes and real-world applications of finding the slope of a line.

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Introduction

In our previous article, we learned how to find the slope of a line given two points. In this article, we will answer some frequently asked questions about finding the slope of a line.

Q&A

Q: What is the formula for finding the slope of a line given two points?

A: The formula for finding the slope of a line given two points is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Q: How do I find the slope of a line if the two points are the same?

A: If the two points are the same, then the slope of the line is undefined. This is because the denominator of the formula (x2 - x1) would be zero, and division by zero is undefined.

Q: Can I find the slope of a line if the two points are not on the same line?

A: No, you cannot find the slope of a line if the two points are not on the same line. The slope of a line is a measure of how steep it is, and if the two points are not on the same line, then they do not have a common slope.

Q: How do I find the slope of a line if one of the points is a vertical line?

A: If one of the points is a vertical line, then the slope of the line is undefined. This is because the denominator of the formula (x2 - x1) would be zero, and division by zero is undefined.

Q: Can I find the slope of a line if the two points are on a vertical line?

A: No, you cannot find the slope of a line if the two points are on a vertical line. The slope of a line is a measure of how steep it is, and if the two points are on a vertical line, then they do not have a common slope.

Q: How do I find the slope of a line if the two points are on a horizontal line?

A: If the two points are on a horizontal line, then the slope of the line is zero. This is because the numerator of the formula (y2 - y1) would be zero, and any number divided by zero is zero.

Q: Can I find the slope of a line if the two points are on a diagonal line?

A: Yes, you can find the slope of a line if the two points are on a diagonal line. The slope of a diagonal line is a measure of how steep it is, and you can find it using the formula m = (y2 - y1) / (x2 - x1).

Q: How do I find the slope of a line if the two points are on a line with a negative slope?

A: If the two points are on a line with a negative slope, then the slope of the line is negative. This is because the numerator of the formula (y2 - y1) would be negative, and any number divided by a negative number is negative.

Q: Can I find the slope of a line if the two points are on a line with a positive slope?

A: Yes, you can find the slope of a line if the two points are on a line with a positive slope. The slope of a line with a positive slope is a measure of how steep it is, and you can find it using the formula m = (y2 - y1) / (x2 - x1).

Tips and Tricks

  • When finding the slope of a line, make sure to use the correct formula: m = (y2 - y1) / (x2 - x1).
  • When plugging in the values into the formula, make sure to use the correct coordinates of the two points.
  • When simplifying the fraction, make sure to divide both the numerator and the denominator by their greatest common divisor.

Common Mistakes

  • Using the wrong formula to find the slope of a line.
  • Plugging in the wrong values into the formula.
  • Not simplifying the fraction correctly.

Real-World Applications

  • Finding the slope of a line is an important concept in mathematics and has many real-world applications, such as:
  • Calculating the rate of change of a quantity over time.
  • Determining the steepness of a hill or a roof.
  • Finding the equation of a line that passes through two points.

Conclusion

In conclusion, finding the slope of a line given two points is an important concept in mathematics. We answered some frequently asked questions about finding the slope of a line and provided tips and tricks for finding the slope of a line. We also discussed common mistakes and real-world applications of finding the slope of a line.