Writing the Equation of the Linear Function

Oct 13, 2025 by windailys.com 23 views

Introduction

In mathematics, a linear function is a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. Given a table of points on the graph of a linear function, we can determine the equation of the function by finding the slope and y-intercept. In this article, we will discuss how to find the equation of a linear function given a table of points.

Understanding the Table

The table given represents some points on the graph of a linear function. The table has two columns, x and y, which represent the input and output values of the function, respectively. The table has four rows, each representing a point on the graph.

x	y
-4	10
-2	7
6	2
89	-5^(-12)

Finding the Slope

To find the equation of the linear function, we need to find the slope (m) and y-intercept (b). The slope is a measure of how steep the line is, and it can be found using the formula:

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

where (x1, y1) and (x2, y2) are two points on the graph.

Let's use the first two points, (-4, 10) and (-2, 7), to find the slope.

m = (7 - 10) / (-2 - (-4)) m = -3 / 2 m = -1.5

Finding the Y-Intercept

Now that we have the slope, we can find the y-intercept (b) by substituting the slope and one of the points into the equation y = mx + b.

Let's use the point (-4, 10) and the slope (-1.5) to find the y-intercept.

10 = (-1.5)(-4) + b 10 = 6 + b b = 4

Writing the Equation of the Linear Function

Now that we have the slope (m = -1.5) and y-intercept (b = 4), we can write the equation of the linear function.

y = -1.5x + 4

Checking the Equation

To check if the equation is correct, we can substitute the points from the table into the equation and see if they satisfy the equation.

For the point (-4, 10):

10 = -1.5(-4) + 4 10 = 6 + 4 10 = 10

For the point (-2, 7):

7 = -1.5(-2) + 4 7 = 3 + 4 7 = 7

For the point (6, 2):

2 = -1.5(6) + 4 2 = -9 + 4 2 = -5

For the point (89, -5^(-12)):

-5^(-12) = -1.5(89) + 4 -5^(-12) = -133.5 + 4 -5^(-12) = -129.5

The equation y = -1.5x + 4 satisfies all the points in the table.

Conclusion

In this article, we discussed how to find the equation of a linear function given a table of points. We found the slope and y-intercept using the formula m = (y2 - y1) / (x2 - x1) and y = mx + b, respectively. We then wrote the equation of the linear function and checked if it satisfied all the points in the table. The equation y = -1.5x + 4 represents the linear function given in the table.

References

[1] Khan Academy. (n.d.). Linear Functions. Retrieved from <https://www.khanacademy.org/math/algebra/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6f7d/x2f6
Q&A: The Table Represents Some Points on the Graph of a Linear Function ====================================================================

Q: What is a linear function?

A: A linear function is a function that can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I find the slope of a linear function?

A: To find the slope of a linear function, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the graph.

Q: How do I find the y-intercept of a linear function?

A: To find the y-intercept of a linear function, you can substitute the slope and one of the points into the equation y = mx + b.

Q: What is the equation of the linear function represented by the table?

A: The equation of the linear function represented by the table is y = -1.5x + 4.

Q: How do I check if the equation is correct?

A: To check if the equation is correct, you can substitute the points from the table into the equation and see if they satisfy the equation.

Q: What if the points do not satisfy the equation?

A: If the points do not satisfy the equation, then the equation is not correct, and you need to recheck your calculations.

Q: Can I use any two points to find the slope?

A: Yes, you can use any two points to find the slope. However, it's best to use points that are close together to get a more accurate slope.

Q: Can I use any point to find the y-intercept?

A: Yes, you can use any point to find the y-intercept. However, it's best to use a point that is on the y-axis (x = 0) to get the y-intercept.

Q: What if the table has more than four points?

A: If the table has more than four points, you can still use the same method to find the equation of the linear function. Just make sure to use the correct points to find the slope and y-intercept.

Q: Can I use this method to find the equation of a non-linear function?

A: No, this method is only for finding the equation of a linear function. If the function is non-linear, you will need to use a different method to find the equation.

Q: Where can I learn more about linear functions?

A: You can learn more about linear functions on websites such as Khan Academy, Mathway, and Wolfram Alpha.

Q: Can I use a calculator to find the equation of a linear function?

A: Yes, you can use a calculator to find the equation of a linear function. Many calculators have a built-in function to find the equation of a linear function.

Q: What if I'm still having trouble finding the equation of a linear function?

A: If you're still having trouble finding the equation of a linear function, you can try asking a teacher or tutor for help. They can provide you with additional guidance and support.