Tomas wrote the equation y 3x 3 4 – Tomas’ equation, y = 3x – 3 + 4, is a fundamental mathematical expression that holds significant importance in various fields. This equation represents a linear function, providing a simple yet powerful tool for understanding the relationship between two variables, x and y.
Delving into its components, operations, and applications, we unravel the intriguing world of Tomas’ equation.
The equation consists of three key elements: the dependent variable y, the independent variable x, and the constants 3 and 4. The variable y represents the output or result of the equation, while x represents the input or independent variable.
The constants 3 and 4 determine the slope and y-intercept of the linear function, respectively.
Equation Analysis: Tomas Wrote The Equation Y 3x 3 4
The equation “y = 3x – 3 + 4” is a linear equation in two variables, x and y. It represents a straight line on a coordinate plane.
The equation consists of three terms: 3x, -3, and 4. The coefficient of x is 3, which means that for every one-unit increase in x, y increases by 3 units.
The constant term, -3 + 4, is the y-intercept of the line. This means that when x is 0, y is -3 + 4 = 1.
The relationship between the variables x and y is linear, which means that the graph of the equation is a straight line.
Mathematical Operations
The mathematical operations involved in the equation are addition and subtraction.
To simplify the equation, we can first combine the constant terms:
“`y = 3x
3 + 4
y = 3x + 1“`
Then, we can factor out the greatest common factor from the variable terms:
“`y = 3(x + 1/3)“`
To solve the equation for x, we can isolate the variable term on one side of the equation and the constant term on the other side:
“`
(x + 1/3) = y
x + 1/3 = y/3x = y/3
1/3
“`
Graphing the Equation, Tomas wrote the equation y 3x 3 4
To graph the equation, we can create a table of values:
| x | y |
|---|---|
| 0 | 1 |
| 1 | 4 |
| 2 | 7 |
We can then plot these points on a coordinate plane and draw a line through them.
The graph of the equation is a straight line with a slope of 3 and a y-intercept of 1.
Applications
The equation “y = 3x – 3 + 4” can be applied to a variety of real-world situations.
For example, it can be used to model the relationship between the number of hours worked and the amount of money earned.
If a person earns $3 per hour, then the equation can be used to calculate the amount of money earned for any number of hours worked.
Extensions
There are a number of variations of the equation “y = 3x – 3 + 4”.
For example, the equation “y = 3x + b” represents a family of lines with different y-intercepts.
The slope of all of these lines is 3, but the y-intercept varies depending on the value of b.
Essential Questionnaire
What is the significance of the constant 3 in the equation?
The constant 3 represents the slope of the linear function. It determines the steepness of the line when graphed.
How do I solve the equation for y when x is equal to 2?
Substitute x = 2 into the equation: y = 3(2) – 3 + 4 = 6 – 3 + 4 = 7. Therefore, when x is equal to 2, y is equal to 7.
What is the y-intercept of the graph of the equation?
The constant 4 represents the y-intercept of the graph. It is the point where the line intersects the y-axis.
