Write The Slope-intercept Equation Of The Function F F F Whose Graph Satisfies The Given Conditions.The Graph Of F F F Passes Through { (-1,9)$}$ And Is Perpendicular To The Line Whose Equation Is X = 19 X = 19 X = 19 .The Equation

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Introduction

In mathematics, the slope-intercept equation of a function is a way to represent the function in the form of y = mx + b, where m is the slope and b is the y-intercept. This equation is useful in various fields, including physics, engineering, and economics. In this article, we will discuss how to write the slope-intercept equation of a function given certain conditions.

Given Conditions

The graph of the function f passes through the point (-1, 9) and is perpendicular to the line whose equation is x = 19. To find the slope-intercept equation of the function, we need to use this information.

Understanding Perpendicular Lines

Two lines are perpendicular if their slopes are negative reciprocals of each other. The equation of the line x = 19 is a vertical line, which means its slope is undefined. However, we can find the slope of the line perpendicular to it by taking the negative reciprocal of the slope of the given line.

Finding the Slope of the Perpendicular Line

Since the slope of the line x = 19 is undefined, the slope of the perpendicular line is also undefined. However, we can find the slope of the line perpendicular to it by taking the negative reciprocal of the slope of the given line. In this case, the slope of the perpendicular line is also undefined.

Finding the Equation of the Perpendicular Line

Since the slope of the perpendicular line is undefined, the equation of the line is x = a, where a is a constant. However, we are given that the graph of the function f passes through the point (-1, 9). This means that the point (-1, 9) lies on the line x = a.

Finding the Value of a

To find the value of a, we can substitute the x-coordinate of the point (-1, 9) into the equation x = a. This gives us:

-1 = a

Finding the Equation of the Perpendicular Line

Now that we have found the value of a, we can write the equation of the perpendicular line as:

x = -1

Finding the Slope-Intercept Equation of the Function

Since the graph of the function f passes through the point (-1, 9) and is perpendicular to the line x = 19, the slope of the function is undefined. However, we can find the slope-intercept equation of the function by using the point-slope form of a linear equation.

Using the Point-Slope Form

The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope. In this case, we can use the point (-1, 9) and the slope m = undefined.

Finding the Slope-Intercept Equation

Substituting the values into the point-slope form, we get:

y - 9 = undefined(x - (-1))

Simplifying the equation, we get:

y - 9 = undefined(x + 1)

Finding the Slope-Intercept Equation

To find the slope-intercept equation, we can rewrite the equation in the form y = mx + b. Since the slope is undefined, we can rewrite the equation as:

y = b

Finding the Value of b

To find the value of b, we can substitute the y-coordinate of the point (-1, 9) into the equation y = b. This gives us:

9 = b

Finding the Slope-Intercept Equation

Now that we have found the value of b, we can write the slope-intercept equation of the function as:

y = 9

Conclusion

In this article, we discussed how to write the slope-intercept equation of a function given certain conditions. We found that the slope of the function is undefined and the slope-intercept equation is y = 9. This equation represents the function f whose graph passes through the point (-1, 9) and is perpendicular to the line x = 19.

References

Glossary

  • Slope-Intercept Equation: A way to represent a function in the form of y = mx + b, where m is the slope and b is the y-intercept.
  • Perpendicular Lines: Two lines are perpendicular if their slopes are negative reciprocals of each other.
  • Point-Slope Form: A way to represent a linear equation in the form of y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
    Slope-Intercept Equation Q&A =============================

Introduction

In our previous article, we discussed how to write the slope-intercept equation of a function given certain conditions. In this article, we will answer some frequently asked questions about the slope-intercept equation.

Q: What is the slope-intercept equation?

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

Q: What is the slope of a function?

A: The slope of a function is a measure of how steep the function is. It is calculated as the ratio of the change in y to the change in x.

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

A: To find the slope of a function, you can use the formula:

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

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

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

A: The y-intercept of a function is the point where the function intersects the y-axis. It is the value of y when x is equal to 0.

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

A: To find the y-intercept of a function, you can substitute x = 0 into the equation of the function.

Q: What is the difference between the slope-intercept equation and the point-slope equation?

A: The slope-intercept equation is in the form of y = mx + b, while the point-slope equation is in the form of y - y1 = m(x - x1). The slope-intercept equation is used to represent a function in a more general form, while the point-slope equation is used to represent a function in a more specific form.

Q: Can a function have a slope of 0?

A: Yes, a function can have a slope of 0. This means that the function is a horizontal line.

Q: Can a function have an undefined slope?

A: Yes, a function can have an undefined slope. This means that the function is a vertical line.

Q: How do I determine if a function is a horizontal or vertical line?

A: To determine if a function is a horizontal or vertical line, you can look at the equation of the function. If the equation is in the form of y = c, where c is a constant, then the function is a horizontal line. If the equation is in the form of x = c, where c is a constant, then the function is a vertical line.

Q: Can a function have both a horizontal and vertical component?

A: No, a function cannot have both a horizontal and vertical component. A function can either be a horizontal line, a vertical line, or a combination of both.

Q: How do I graph a function?

A: To graph a function, you can use a graphing calculator or a computer program. You can also use a piece of graph paper and a pencil to draw the graph of the function.

Q: What are some common mistakes to avoid when graphing a function?

A: Some common mistakes to avoid when graphing a function include:

  • Not using a scale on the graph
  • Not labeling the axes
  • Not including the y-intercept
  • Not including the x-intercept
  • Not including the asymptotes

Conclusion

In this article, we answered some frequently asked questions about the slope-intercept equation. We hope that this article has been helpful in understanding the slope-intercept equation and how to use it to represent a function.

References

Glossary

  • Slope-Intercept Equation: A way to represent a function in the form of y = mx + b, where m is the slope and b is the y-intercept.
  • Slope: A measure of how steep a function is.
  • Y-Intercept: The point where a function intersects the y-axis.
  • Point-Slope Equation: A way to represent a linear equation in the form of y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
  • Horizontal Line: A line that is parallel to the x-axis.
  • Vertical Line: A line that is parallel to the y-axis.