The equation of a line is [tex]$y=5 x+1$[/tex]. What is the slope of the line?
a. 5
b. 1
c. -5
d. -1
Answer (1)
The equation is in slope-intercept form: y = m x + b .
Identify the coefficient of x as the slope.
The coefficient of x in y = 5 x + 1 is 5.
The slope of the line is 5 .
Explanation
Understanding the Problem The equation of the line is given as y = 5 x + 1 . We need to determine the slope of this line.
Recalling Slope-Intercept Form The equation is in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept of the line.
Identifying the Slope In the given equation y = 5 x + 1 , we can identify the coefficient of x as the slope of the line. The coefficient of x is 5.
Conclusion Therefore, the slope of the line is 5.
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. Knowing the slope helps in making informed decisions and predictions in various fields.
