Solving for y in a Linear Function

Oct 13, 2025 by ludoplayers7.com 94 views

Solving for y in a Linear Function

In mathematics, a linear function is a polynomial function of degree one, which means it has the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. The linear function $y = 3x + 2$ is a specific example of this type of function, where the slope is $3$ and the y-intercept is $2$ . In this article, we will determine the values of $y$ that correspond to the linear function $y = 3x + 2$ for the given values of $x$ .

The Linear Function

The linear function $y = 3x + 2$ can be written as:

F(x) = 3x + 2

This function takes an input value $x$ and returns an output value $y$ .

Given Values of x

The given values of $x$ are:

$x$	$y$
-1
0
1

We need to determine the corresponding values of $y$ for these values of $x$ .

Solving for y

To solve for $y$ , we can plug in the values of $x$ into the linear function $y = 3x + 2$ .

For x = -1

y = 3(-1) + 2

y = -3 + 2

y = -1

So, the value of $y$ for $x = -1$ is $-1$ .

For x = 0

y = 3(0) + 2

y = 0 + 2

y = 2

So, the value of $y$ for $x = 0$ is $2$ .

For x = 1

y = 3(1) + 2

y = 3 + 2

y = 5

So, the value of $y$ for $x = 1$ is $5$ .

In this article, we determined the values of $y$ that correspond to the linear function $y = 3x + 2$ for the given values of $x$ . We used the linear function to solve for $y$ for each value of $x$ and found that the values of $y$ are $-1$ , $2$ , and $5$ for $x = -1$ , $x = 0$ , and $x = 1$ , respectively.

$x$	$y$
-1	-1
0	2
1	5

This table shows the values of $x$ and the corresponding values of $y$ for the linear function $y = 3x + 2$ .
Frequently Asked Questions (FAQs) about Linear Functions

In our previous article, we discussed the linear function $y = 3x + 2$ and determined the values of $y$ that correspond to the given values of $x$ . In this article, we will answer some frequently asked questions (FAQs) about linear functions.

Q: What is a linear function?

A: A linear function is a polynomial function of degree one, which means it has the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Q: What is the slope of a linear function?

A: The slope of a linear function is the coefficient of the $x$ term, which is $m$ in the equation $y = mx + b$ . In the linear function $y = 3x + 2$ , the slope is $3$ .

Q: What is the y-intercept of a linear function?

A: The y-intercept of a linear function is the value of $y$ when $x = 0$ , which is $b$ in the equation $y = mx + b$ . In the linear function $y = 3x + 2$ , the y-intercept is $2$ .

Q: How do I determine the values of $y$ for a linear function?

A: To determine the values of $y$ for a linear function, you can plug in the values of $x$ into the linear function and solve for $y$ .

Q: What is the difference between a linear function and a quadratic function?

A: A linear function has the form $y = mx + b$ , while a quadratic function has the form $y = ax^2 + bx + c$ . Linear functions have a straight line graph, while quadratic functions have a parabolic graph.

Q: Can a linear function have a negative slope?

A: Yes, a linear function can have a negative slope. For example, the linear function $y = -3x + 2$ has a negative slope of $-3$ .

Q: Can a linear function have a fractional slope?

A: Yes, a linear function can have a fractional slope. For example, the linear function $y = \frac{1}{2}x + 2$ has a fractional slope of $\frac{1}{2}$ .

Q: Can a linear function have a slope of zero?

A: Yes, a linear function can have a slope of zero. For example, the linear function $y = 2$ has a slope of zero.

Q: Can a linear function have a negative y-intercept?

A: Yes, a linear function can have a negative y-intercept. For example, the linear function $y = 3x - 2$ has a negative y-intercept of $-2$ .

Q: Can a linear function have a fractional y-intercept?

A: Yes, a linear function can have a fractional y-intercept. For example, the linear function $y = 3x + \frac{1}{2}$ has a fractional y-intercept of $\frac{1}{2}$ .

In this article, we answered some frequently asked questions (FAQs) about linear functions. We discussed the definition of a linear function, the slope and y-intercept of a linear function, and how to determine the values of $y$ for a linear function. We also discussed the differences between linear and quadratic functions, and the possibility of a linear function having a negative slope, fractional slope, slope of zero, negative y-intercept, and fractional y-intercept.