Find The Missing Value So That The Line Passing Through The Two Points Has The Given Slope.Points: ( 12 , − 12 (12, -12 ( 12 , − 12 ] And ( 7 , Y (7, Y ( 7 , Y ] Slope: − 3 -3 − 3 Select The Correct Response:A. 18 B. 15 C. 6 D. 3

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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. Given two points and a slope, we can find the missing value that makes the line pass through those points with the given slope. In this article, we will explore how to find the missing value for a given slope using the points (12,−12)(12, -12) and (7,y)(7, y) with a slope of −3-3.

Understanding the Slope Formula

The slope formula is given by:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

where mm is the slope, and (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the two points on the line.

Applying the Slope Formula

We are given the points (12,−12)(12, -12) and (7,y)(7, y), and the slope m=−3m = -3. We can plug these values into the slope formula:

−3=y−(−12)7−12-3 = \frac{y - (-12)}{7 - 12}

Simplifying the Equation

Simplifying the equation, we get:

−3=y+12−5-3 = \frac{y + 12}{-5}

Solving for y

To solve for yy, we can multiply both sides of the equation by −5-5:

15=y+1215 = y + 12

Finding the Missing Value

Subtracting 1212 from both sides of the equation, we get:

y=3y = 3

Conclusion

Therefore, the missing value that makes the line pass through the points (12,−12)(12, -12) and (7,y)(7, y) with a slope of −3-3 is y=3y = 3.

Final Answer

The correct answer is:

  • D. 3

Discussion

This problem requires the application of the slope formula to find the missing value. The slope formula is a fundamental concept in mathematics, and understanding how to apply it is essential for solving problems involving lines and slopes. In this article, we have demonstrated how to find the missing value for a given slope using the points (12,−12)(12, -12) and (7,y)(7, y) with a slope of −3-3.

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Introduction

In our previous article, we explored how to find the missing value for a given slope using the points (12,−12)(12, -12) and (7,y)(7, y) with a slope of −3-3. In this article, we will answer some frequently asked questions related to finding the missing value for a given slope.

Q&A

Q: What is the slope formula?

A: The slope formula is given by:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

where mm is the slope, and (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the two points on the line.

Q: How do I apply the slope formula to find the missing value?

A: To apply the slope formula, you need to plug in the values of the two points and the slope into the formula. Then, simplify the equation and solve for the missing value.

Q: What if the slope is zero?

A: If the slope is zero, it means that the line is horizontal. In this case, the missing value is the same as the y-coordinate of one of the points.

Q: What if the slope is undefined?

A: If the slope is undefined, it means that the line is vertical. In this case, the missing value is the same as the x-coordinate of one of the points.

Q: Can I use the slope formula to find the missing value for a line with more than two points?

A: Yes, you can use the slope formula to find the missing value for a line with more than two points. However, you need to use the formula for each pair of points separately and then find the common value.

Q: How do I check if my answer is correct?

A: To check if your answer is correct, you can plug it back into the slope formula and see if it satisfies the equation.

Example Problems

Problem 1:

Find the missing value for a line with a slope of 22 and the points (3,5)(3, 5) and (7,y)(7, y).

Solution:

Using the slope formula, we get:

2=y−57−32 = \frac{y - 5}{7 - 3}

Simplifying the equation, we get:

2=y−542 = \frac{y - 5}{4}

Multiplying both sides of the equation by 44, we get:

8=y−58 = y - 5

Adding 55 to both sides of the equation, we get:

y=13y = 13

Therefore, the missing value is y=13y = 13.

Problem 2:

Find the missing value for a line with a slope of −1-1 and the points (2,3)(2, 3) and (x,5)(x, 5).

Solution:

Using the slope formula, we get:

−1=5−3x−2-1 = \frac{5 - 3}{x - 2}

Simplifying the equation, we get:

−1=2x−2-1 = \frac{2}{x - 2}

Multiplying both sides of the equation by x−2x - 2, we get:

−x+2=2-x + 2 = 2

Adding xx to both sides of the equation, we get:

2=x2 = x

Therefore, the missing value is x=2x = 2.

Conclusion

Finding the missing value for a given slope is an essential concept in mathematics. By understanding how to apply the slope formula, you can solve problems involving lines and slopes. In this article, we have answered some frequently asked questions related to finding the missing value for a given slope and provided example problems to help you practice.