Write the equation of the line that passes through the points (-7,5) and (-7,–8). Put yo answer in fully reduced point-slope form, unless it is a vertical orfiorizontal line.
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.
![### Writing the Equation of a Line
**Problem Statement:**
Write the equation of the line that passes through the points \((-7, 5)\) and \((-7, -8)\). Put your answer in fully reduced point-slope form unless it is a vertical or horizontal line.
**Answer Input:**
- There is a text box where you can input the answer.
- Next to the text box is a 'Submit Answer' button.
**Details on Interface:**
- The text box is where students can type their calculated answer.
- The 'Submit Answer' button allows students to submit their response for assessment.
- There is an indication that this is the first attempt out of 2.
### Additional Instructions:
When approaching this problem, students should remember the following steps:
1. **Identify the Points:** The line passes through points (-7, 5) and (-7, -8).
2. **Determine the Slope \(m\):**
- For vertical lines, like in this case, the x-coordinate for both points is the same (\(-7\)), which means the slope is undefined.
3. **Equation of Vertical Line:**
- Since the line is vertical and passes through \(x = -7\), the equation is simply \(x = -7\).
Therefore, for this particular problem, the line's equation in its appropriate form is:
\[ x = -7 \]
Students should then type this equation into the text box and click "Submit Answer" to have their response evaluated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21d1b41c-6e6f-443d-8501-baba3fa0c5ca%2F0d2ed491-8288-449f-afe6-cd42dc246a76%2Ftgi6j2x_processed.jpeg&w=3840&q=75)
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