13. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no ra The river was 60 feet before the drought began. (4 points)
a. What is the rate of change (slope) for this scenario?
b. What is the y-intercept for this scenario?
c. Write an equation for the scenario in slope-intercept form.
d. Write an equation in standard form
5z + v = 60
a - 5x + w = 60
31 - 5
#5
# (0, 60)
# (0, - 5)
u = 5x + 45
# (- 5, 0)
#15
# 5x + y = 35
y = - 5x + 60
11 y = - 5x - 35
a. The rate of change (slope) for this scenario is -5.
b. The y-intercept for this scenario is 60.
c. The equation for the scenario in slope-intercept form is y = -5x + 60.
d. The equation in standard form is 5x + y = 60.
a. To find the rate of change (slope), we can use the formula:
slope = (change in y) / (change in x)
In this scenario, the change in y is from 60 feet to 10 feet, which is a decrease of 50 feet. The change in x is from 0 days to 10 days, which is an increase of 10 days.
slope = (10 - 60) / (10 - 0) = -50 / 10 = -5
So, the rate of change (slope) for this scenario is -5.
b. The y-intercept is the value of y when x is 0. In this scenario, when there are 0 days of no rain, the water level is 60 feet. Therefore, the y-intercept is 60.
c. The equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting the values, we get:
y = -5x + 60
So, the equation for the scenario in slope-intercept form is y = -5x + 60.
d. The standard form of an equation is Ax + By = C, where A, B, and C are constants.
To convert the equation y = -5x + 60 to standard form, we need to rearrange it:
5x + y = 60
So, the equation in standard form is 5x + y = 60.
To answer these questions, we need to analyze the given information step by step:
a. The rate of change (slope) represents how much the water level decreases or increases over time. In this case, we can determine the rate of change by finding the difference in water level over the given time period. Subtracting the initial water level (60 feet) from the final water level after 3 days (45 feet), we get a decrease of 15 feet. So, the rate of change (slope) is -15 feet per 3 days.
b. The y-intercept represents the point where the line intersects the y-axis. In this scenario, the y-intercept would be the water level when there is no drought or time has elapsed. Since the initial water level is given as 60 feet, the y-intercept is 60.
c. To write the equation in slope-intercept form (y = mx + b), we use the values we have determined. The slope (m) is -15 feet per 3 days, and the y-intercept (b) is 60. Therefore, the equation is y = -15/3x + 60, which simplifies to y = -5x + 60.
d. To write the equation in standard form (Ax + By = C), we need to rearrange the equation y = -5x + 60. First, we get rid of the fraction by multiplying every term by 3, resulting in 3y = -15x + 180. Next, we bring all the terms to one side of the equation and arrange them in standard form. Doing this, we get 15x + 3y = 180.
So, the correct equation in standard form is 15x + 3y = 180.
Please note that the equation options provided in the question, such as "5z + v = 60" and "a - 5x + w = 60," do not relate to the given scenario and are not the correct equations for this situation.