Q10 Compare slopes Homework • Unanswered Fill in the Blanks Type your answers in all of the blanks and submit Write each equation in slope-intercept form. Do not enter spaces in your answer. Then identify the slope of each line. Use/to enter a fraction if needed. Then state how the slopes of the lines relate. Equation 1:3x - y= -9and Equation 2: 6x + 2y = 12 a. Equation 1 in slope-intercept form: Type your answer here b. Slope of equation 1: Type your answer here c. Equation 2 in slope-intercept form: Type your answer here d. Slope of equation 2: Type your answer here e. The slopes of the two equations are Type your answer here .(Enter equal, reciprocals, negative reciprocals, opposites, or none of these in the blank.)
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.
![### Comparing Slopes
#### Homework Assignment: Due in 11 hours
You are tasked with comparing the slopes of two linear equations. Follow the instructions below to complete this assignment.
#### Instructions:
1. **Write each equation in slope-intercept form (y = mx + b).**
- **Do not enter spaces in your answer.**
2. **Identify the slope (m) of each line.**
- Use a slash (/) to enter a fraction if needed.
3. **State how the slopes of the lines relate (equal, reciprocals, negative reciprocals, opposites, or none of these).**
#### Equations:
- **Equation 1:** \( 3x - y = -9 \)
- **Equation 2:** \( 6x + 2y = 12 \)
#### Questions:
a. **Equation 1 in slope-intercept form:**
*\[ \text{Type your answer here} \]*
b. **Slope of Equation 1:**
*\[ \text{Type your answer here} \]*
c. **Equation 2 in slope-intercept form:**
*\[ \text{Type your answer here} \]*
d. **Slope of Equation 2:**
*\[ \text{Type your answer here} \]*
e. **The slopes of the two equations are:**
*\[ \text{Type your answer here} \]* (equal, reciprocals, negative reciprocals, opposites, or none of these)
#### Example:
For practice, let’s solve an example:
- Given Equation: \( 4x - 2y = 8 \)
To convert this into slope-intercept form:
\[ 4x - 2y = 8 \]
\[ -2y = -4x + 8 \]
\[ y = 2x - 4 \]
The slope \( m \) is 2.
Proceed with your homework based on this methodology.
Remember, you have 3 attempts to answer correctly. Make sure to review your calculations before submitting. Good luck!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F066a8f6b-0850-46b7-9749-7f575952e384%2Fc5219c83-e6fe-447f-b702-e381bedd32f5%2Fy5rkcz_processed.jpeg&w=3840&q=75)
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