Write a sentence explaining the meaning of the slope and y-intercept for the given linear relation.
According to the Statistical Abstract of the United States, the number of crimes, C, reported since 1998 is given by the equation: C=31000-29t where t is in years.
A. What is the value and physical meaning of the slope?
I have "Reported crimes decreases to 2900 over the years".
B. What is the value and physical meaning of the y-intercept?
I have "Reported crimes in 1998 were 3100".
I am sure I am off by a lot, but any help with this is greatly appreciated. Thanks!
the slope is -29 crimes per year
In other words the number of crimes decreases by 29 every year.
when t = 0, C = 31,000. That is the number of crimes when the equation started in 1998
I suspect the 31,000 is a typo as is the 29
3100 is correct, the typo is 2900. Thank you for helping.
A. The slope of the linear equation C=31000-29t is -29. The physical meaning of the slope is that for every one year that passes, the number of reported crimes decreases by 29.
B. The y-intercept of the linear equation C=31000-29t is 31000. The physical meaning of the y-intercept is that in the year 1998 (when t=0), there were 31000 reported crimes.
A. The slope of the linear equation C = 31,000 - 29t represents the rate of change of reported crimes over time. In this case, since the slope is -29, it means that for every passing year, the number of reported crimes decreases by an average of 29.
To obtain the slope, you can observe that the given equation is in the form y = mx + b, where y represents the dependent variable (C in this case), x represents the independent variable (t in this case), m represents the slope, and b represents the y-intercept. By directly comparing the equation to the form y = mx + b, you can identify the slope as the coefficient of the independent variable, which is -29 in this case.
B. The y-intercept of the linear equation C = 31,000 - 29t represents the initial value of reported crimes. In other words, it represents the number of reported crimes in the starting year, which is 1998 in this case.
To determine the y-intercept, you can observe that the given equation is in the form y = mx + b. By comparing the equation to this form, you can identify the y-intercept as the constant term, which is 31,000 in this case.
Therefore, the correct interpretations are:
A. The slope is -29, which means that on average, the number of reported crimes decreases by 29 each year.
B. The y-intercept is 31,000, indicating that there were 31,000 reported crimes in the starting year, which is 1998.