Find the slope of the line shown on the graph to the right. The slope of the line is. (Type an integer or a simplified fraction.) 4- 2- -10-81-61-4-2: 4:6810
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.
![### Understanding the Slope of a Line
#### Problem Statement
Find the slope of the line shown on the graph to the right.
#### Input Box
The slope of the line is [ ]
(Type an integer or a simplified fraction.)
#### Instructions
Enter your answer in the answer box and then click Check Answer.
#### Diagram Description
The graph provided shows a straight line sloping upwards from left to right. The grid is labeled with the X-axis ranging from -10 to 10 and the Y-axis ranging from -10 to 10. The line intersects the graph at specific points. The exact coordinates of the intersection points are not labeled but can be visually estimated as they cross through the grid intersections.
- **X-Axis**: Horizontal axis marked from -10 to 10.
- **Y-Axis**: Vertical axis marked from -10 to 10.
- **Line**: Slopes upward from the lower left to the upper right, indicating a positive slope.
#### How to Find the Slope
To determine the slope (**m**) of the line:
1. **Identify two points on the line**: Choose any two points through which the line passes directly on the graph.
2. **Use the slope formula**:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]
Where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.
3. **Simplify your answer**: Express the slope as an integer or a simplified fraction.
### Example
Suppose we select points (2, 3) and (4, 7):
1. The coordinates are \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (4, 7) \).
2. Substitute into the formula:
\[
m = \frac{{7 - 3}}{{4 - 2}} = \frac{4}{2} = 2
\]
Therefore, the slope of the line is 2.
By following these steps, you can determine the slope of the line shown in the diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad9e6bab-9852-4973-9ccc-3bd612bcaff6%2F9c00226b-343c-4c89-ba47-553aa3b921e2%2F9z693c8_processed.jpeg&w=3840&q=75)
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