Find the slope for the following equation:
[tex]$y=-\frac{2 x}{3}+4$[/tex]
Answer (1)
Identify the equation: y = − 3 2 x + 4 .
Recall the slope-intercept form: y = m x + b , where m is the slope.
Determine the slope by comparing the given equation with the slope-intercept form.
The slope of the equation is − 3 2 .
Explanation
Identify the equation The given equation is y = − 3 2 x + 4 . We need to identify the slope of this equation.
Recall slope-intercept form The slope-intercept form of a linear equation is given by y = m x + b , where m represents the slope and b represents the y-intercept.
Determine the slope Comparing the given equation y = − 3 2 x + 4 with the slope-intercept form y = m x + b , we can see that the coefficient of x is − 3 2 . Therefore, the slope m is − 3 2 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, if you are analyzing the steepness of a hill on a map, the slope tells you how much the elevation changes for every unit of horizontal distance. Similarly, in economics, the slope of a cost function can represent the marginal cost, indicating how much the cost increases for each additional unit produced. Linear equations and their slopes are fundamental in modeling and understanding rates of change in various fields.
