The graph of y=3x-4 is a straight line that is commonly used in mathematics. It is a linear equation that represents a relationship between two variables; x and y. In this article, we will look at how to graph this equation and what it represents.
The Slope-Intercept Form
The equation y=3x-4 is in the slope-intercept form. This means that the equation can be written as y=mx+b, where m is the slope of the line and b is the y-intercept. In this equation, the slope is 3 and the y-intercept is -4.
Graphing the Equation
To graph the equation y=3x-4, we first plot the y-intercept on the y-axis. The y-intercept is the point where the line crosses the y-axis, which in this case is -4. Then, we use the slope to find another point on the line. Since the slope is 3, we can move three units up and one unit to the right from the y-intercept to get another point on the line. We can continue to do this to get more points on the line and then connect them to form a straight line.
The Meaning of the Graph
The graph of y=3x-4 represents a linear relationship between two variables. In this case, x represents the independent variable and y represents the dependent variable. The slope of the line represents the rate of change of y with respect to x. In other words, for every one unit increase in x, y increases by 3 units. The y-intercept represents the value of y when x is equal to zero.
Positive Slope
Since the slope of the line is positive, the line slopes upward from left to right. This means that as x increases, y also increases. This is because the rate of change of y with respect to x is positive.
Applications of the Graph
The graph of y=3x-4 has many applications in real life. For example, it can be used to represent the relationship between the number of hours worked and the amount of money earned. In this case, x represents the number of hours worked and y represents the amount of money earned. The slope of the line represents the hourly rate of pay and the y-intercept represents the minimum amount of money earned.
Parallel Lines
If we graph another line that has the same slope as y=3x-4, the two lines will be parallel. This is because parallel lines have the same slope. However, the y-intercept of the second line may be different.
Perpendicular Lines
If we graph another line that is perpendicular to y=3x-4, the two lines will intersect at a right angle. This is because perpendicular lines have slopes that are negative reciprocals of each other. In this case, the slope of the perpendicular line would be -1/3.
Conclusion
In conclusion, the graph of y=3x-4 is a straight line that represents a linear relationship between two variables. It has many applications in real life and can be used to model various situations. By understanding the slope-intercept form and how to graph the equation, we can gain a better understanding of the meaning of the graph and how it can be used.
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