Write a linear function that passes through the point (-2,3)whose slope is m -5. Enter the function in the form f(x) = mx + b. Do not enter any blank spaces in your answer.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![**Educational Exercise**
**Topic: Slope-Intercept Form**
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### Substituting the given values into the slope-intercept form
To find the equation of a line in slope-intercept form, use the formula:
\[ y = mx + b \]
Given:
\[ y = -6 \]
\[ m = \frac{1}{5} \]
\[ x = 5 \]
Substitute the given values into the formula:
\[ -6 = \frac{1}{5}(5) + b \]
Calculation:
\[ -6 = 1 + b \]
Solve for \( b \):
\[ b = -6 - 1 \]
\[ b = -7 \]
Answer:
\[ y = \frac{1}{5}x - 7 \]
**Status:**
- Answered: Correct
- 2 attempts left
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**Q27: Slope-Intercept Form**
**Type: Homework**
**Status: Unanswered**
**Problem Statement:**
Write a linear function that passes through the point \((-2, -3)\) whose slope is \( m = -5 \). Enter the function in the form \( f(x) = mx + b \). Do not enter any blank spaces in your answer.
**Answer Section:**
\( \text{Type your answer and submit:} \)
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**Q28: Slope-Intercept Form**
**Type: Homework**
**Status: Unanswered**
**Problem Statement:**
Write a linear function whose graph passes through the point \( (4, -2) \) and has a slope of 0. Enter the function in the form \( f(x)=mx+b \). Do not enter any blank spaces in your answer.
**Answer Section:**
\( \text{Type your answer and submit:} \)
**Note:** Ensure to provide accurate answers by carefully calculating the values and avoid any blank spaces in your response.
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**Attempts Remaining:**
- Q27: Unanswered - 3 attempts left
- Q28: Unanswered - 3 attempts left
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This exercise helps in understanding how to derive the equation of a line using the slope-intercept form. Practice by solving similar problems to enhance your skill in determining the slope and intercepts effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F066a8f6b-0850-46b7-9749-7f575952e384%2Fc527aa6d-a856-4e55-9654-262537cb06bf%2Fz9xbu6_processed.jpeg&w=3840&q=75)
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