Given The Function Y = − 2 X − 5 Y = -2x - 5 Y = − 2 X − 5 , Plot All Of The Ordered Pairs For The Values In The Domain D : { − 6 , − 5 , − 2 , 0 , 1 } D: \{-6, -5, -2, 0, 1\} D : { − 6 , − 5 , − 2 , 0 , 1 } .

Introduction

In mathematics, a linear function is a function that can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The graph of a linear function is a straight line that passes through the point $(0, b)$. In this article, we will explore the graph of the linear function $y = -2x - 5$ by plotting all of the ordered pairs for the values in the domain $D: \{-6, -5, -2, 0, 1\}$.

Understanding the Domain

The domain of a function is the set of all possible input values for which the function is defined. In this case, the domain is given as $D: \{-6, -5, -2, 0, 1\}$. This means that we will be finding the corresponding output values for each of these input values.

Finding the Ordered Pairs

To find the ordered pairs, we need to substitute each value in the domain into the function $y = -2x - 5$ and calculate the corresponding output value.

Substituting -6 into the Function

x = -6
y = -2 * x - 5
print(f"(-6, {y})")

When we substitute $x = -6$ into the function, we get:

$y = -2(-6) - 5$ $y = 12 - 5$ $y = 7$

So, the ordered pair for $x = -6$ is $(-6, 7)$.

Substituting -5 into the Function

x = -5
y = -2 * x - 5
print(f"(-5, {y})")

When we substitute $x = -5$ into the function, we get:

$y = -2(-5) - 5$ $y = 10 - 5$ $y = 5$

So, the ordered pair for $x = -5$ is $(-5, 5)$.

Substituting -2 into the Function

x = -2
y = -2 * x - 5
print(f"(-2, {y})")

When we substitute $x = -2$ into the function, we get:

$y = -2(-2) - 5$ $y = 4 - 5$ $y = -1$

So, the ordered pair for $x = -2$ is $(-2, -1)$.

Substituting 0 into the Function

x = 0
y = -2 * x - 5
print(f"(0, {y})")

When we substitute $x = 0$ into the function, we get:

$y = -2(0) - 5$ $y = 0 - 5$ $y = -5$

So, the ordered pair for $x = 0$ is $(0, -5)$.

Substituting 1 into the Function

x = 1
y = -2 * x - 5
print(f"(1, {y})")

When we substitute $x = 1$ into the function, we get:

$y = -2(1) - 5$ $y = -2 - 5$ $y = -7$

So, the ordered pair for $x = 1$ is $(1, -7)$.

Plotting the Ordered Pairs

Now that we have found all of the ordered pairs, we can plot them on a coordinate plane.

x	y
-6	7
-5	5
-2	-1
0	-5
1	-7

The graph of the linear function $y = -2x - 5$ is a straight line that passes through the points $(-6, 7)$, $(-5, 5)$, $(-2, -1)$, $(0, -5)$, and $(1, -7)$.

Conclusion

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Q: What is a linear function?

A: A linear function is a function that can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The graph of a linear function is a straight line that passes through the point $(0, b)$.

Q: What is the domain of a linear function?

A: The domain of a linear function is the set of all possible input values for which the function is defined. In other words, it is the set of all possible values of $x$.

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

A: To find the ordered pairs of a linear function, you need to substitute each value in the domain into the function and calculate the corresponding output value.

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 $y = mx + b$. The slope represents the rate of change of the function.

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

A: The y-intercept of a linear function is the value of $b$ in the equation $y = mx + b$. The y-intercept represents the point where the function intersects the y-axis.

Q: How do I plot the graph of a linear function?

A: To plot the graph of a linear function, you need to plot the ordered pairs on a coordinate plane. You can use a ruler or a graphing calculator to help you plot the points.

Q: What is the equation of a linear function?

A: The equation of a linear function is in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

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

A: To find the equation of a linear function, you need to find the slope and the y-intercept. You can use the ordered pairs to find the slope and the y-intercept.

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

A: A linear function is a function that can be written in the form $y = mx + b$, while a quadratic function is a function that can be written in the form $y = ax^2 + bx + c$. The graph of a linear function is a straight line, while the graph of a quadratic function is a parabola.

Q: Can a linear function have a negative slope?

A: Yes, a linear function can have a negative slope. A negative slope means that the function is decreasing as $x$ increases.

Q: Can a linear function have a zero slope?

A: Yes, a linear function can have a zero slope. A zero slope means that the function is a horizontal line.

Q: Can a linear function have a fractional slope?

A: Yes, a linear function can have a fractional slope. A fractional slope means that the function is increasing or decreasing at a rate that is not a whole number.

Conclusion

In this article, we answered some frequently asked questions about linear functions. We covered topics such as the definition of a linear function, the domain of a linear function, and how to find the ordered pairs of a linear function. We also discussed the slope and y-intercept of a linear function, and how to plot the graph of a linear function.