Use the points shown on the graph to find the slope of the 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.
![**Finding the Slope of a Line Using a Graph**
To find the slope of the line shown in the graph, follow the steps below:
1. **Identify the Points**: Look at the graph to note the coordinates of two points the line passes through. In this graph, the points are approximately (-5, 6) and (5, -3).
2. **Calculate the Slope**:
- Use the slope formula:
\[\text{Slope} (m) = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}\]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
- Substitute the points into the formula:
\[m = \frac{-3 - 6}{5 - (-5)} = \frac{-3 - 6}{5 + 5} = \frac{-9}{10}\]
Therefore, the slope \(m\) of the line is \(\frac{-9}{10}\) or -0.9.
3. **Answer Choices**:
- **A. The slope is [ ]**: You will input \(-0.9\) into the answer box.
- **B. The slope is undefined**: This is not correct for this line as it has a calculable slope.
### Graph Description:
- The graph has labeled x and y axes with values spanning from -6 to 6.
- The line shown is descending from left to right, indicating a negative slope.
- The grid lines help in identifying the coordinates of the points the line intersects.
After entering the slope in the answer box, click "Check Answer." If needed, you can clear the answer input with "Clear All."
### Additional Tools:
There are options provided to input different types of mathematical symbols and functions using the buttons below the answer box.
**Interactive Features**: Users can select, enter, and verify their answers using the provided interactive features of the platform.
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