Which Table Represents A Linear Function That Has A Slope Of 5 And A $y$-intercept Of 20? \[ \begin{tabular}{|c|c|} \hline X$ & Y Y Y \ \hline -4 & 0 \ \hline 0 & 20 \ \hline 4 & 40 \ \hline 8 & 60
Which Table Represents a Linear Function with a Slope of 5 and a y-Intercept of 20?
In mathematics, a linear function is a type of function that can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear function represents the rate of change of the function with respect to the input variable, while the y-intercept represents the point at which the function intersects the y-axis. In this article, we will explore which table represents a linear function with a slope of 5 and a y-intercept of 20.
A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear function represents the rate of change of the function with respect to the input variable, while the y-intercept represents the point at which the function intersects the y-axis. For example, the linear function y = 2x + 3 has a slope of 2 and a y-intercept of 3.
The slope of a linear function is a measure of how much the function changes as the input variable changes. In other words, it represents the rate of change of the function. The y-intercept of a linear function represents the point at which the function intersects the y-axis. In this article, we are given a linear function with a slope of 5 and a y-intercept of 20.
We are given four tables to choose from, each representing a different linear function. We need to determine which table represents a linear function with a slope of 5 and a y-intercept of 20.
| Table 1 | Table 2 | Table 3 | Table 4 |
|---|---|---|---|
| x | y | x | y |
| -4 | 0 | -4 | 20 |
| 0 | 20 | 0 | 40 |
| 4 | 40 | 4 | 60 |
| 8 | 60 | 8 | 80 |
Table 1
| x | y |
|---|---|
| -4 | 0 |
| 0 | 20 |
| 4 | 40 |
| 8 | 60 |
Table 2
| x | y |
|---|---|
| -4 | 20 |
| 0 | 40 |
| 4 | 60 |
| 8 | 80 |
Table 3
| x | y |
|---|---|
| -4 | 0 |
| 0 | 20 |
| 4 | 40 |
| 8 | 60 |
Table 4
| x | y |
|---|---|
| -4 | 20 |
| 0 | 40 |
| 4 | 60 |
| 8 | 80 |
To determine which table represents a linear function with a slope of 5 and a y-intercept of 20, we need to analyze each table and determine if it meets the given conditions.
Table 1
The table has a y-intercept of 20, which meets the given condition. However, we need to determine if the slope is 5. To do this, we can calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Using the points (0, 20) and (4, 40), we get m = (40 - 20) / (4 - 0) = 20 / 4 = 5. Therefore, Table 1 represents a linear function with a slope of 5 and a y-intercept of 20.
In conclusion, Table 1 represents a linear function with a slope of 5 and a y-intercept of 20. The table meets the given conditions and has a slope of 5 and a y-intercept of 20. Therefore, Table 1 is the correct table.
The final answer is Table 1.
Frequently Asked Questions (FAQs) about Linear Functions
In our previous article, we discussed how to determine which table represents a linear function with a slope of 5 and a y-intercept of 20. In this article, we will answer some frequently asked questions (FAQs) about linear functions.
A: A linear function is a type of function that can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.
A: The slope of a linear function represents the rate of change of the function with respect to the input variable.
A: The y-intercept of a linear function represents the point at which the function intersects the y-axis.
A: To determine the slope and y-intercept of a linear function, you can use the formula y = mx + b, where m is the slope and b is the y-intercept. You can also use the points on the graph to calculate the slope and y-intercept.
A: A linear function is a function that can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. A non-linear function is a function that cannot be represented in this form.
A: Yes, a linear function can have a negative slope. For example, the linear function y = -2x + 3 has a negative slope of -2.
A: Yes, a linear function can have a zero slope. For example, the linear function y = 0x + 2 has a zero slope.
A: Yes, a linear function can have a fractional slope. For example, the linear function y = 1/2x + 2 has a fractional slope of 1/2.
A: Yes, a linear function can have a negative y-intercept. For example, the linear function y = 2x - 3 has a negative y-intercept of -3.
A: Yes, a linear function can have a fractional y-intercept. For example, the linear function y = 2x + 1/2 has a fractional y-intercept of 1/2.
In conclusion, linear functions are an important concept in mathematics and have many applications in real-world problems. We hope that this article has helped to answer some of the frequently asked questions about linear functions.
The final answer is that linear functions are a type of function that can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.