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 rain. The river was 60 feet before the drought began.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a. What is the rate of change (slope) for this scenario? Response area b. What is the y-intercept for this scenario? Response area c. Write an equation for the scenario in slope-intercept form. Response area d. Write an equation in standard form. Response area
a. What is the rate of change (slope) for this scenario?
The rate of change can be calculated using the formula: slope = (change in y)/(change in x).
Using the given values:
change in y = 10 - 45 = -35
change in x = 10 - 3 = 7
slope = (-35)/(7) = -5
Therefore, the rate of change (slope) for this scenario is -5.
b. What is the y-intercept for this scenario?
The y-intercept is the value of y when x is 0. In this scenario, when there is no drought (x=0), the water level is 60 feet.
Therefore, the y-intercept for this scenario is 60.
c. Write an equation for the scenario in slope-intercept form.
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Using the values from the scenario, the equation would be:
y = -5x + 60
d. Write an equation in standard form.
The standard form of an equation is Ax + By = C, where A, B, and C are constants.
To write the equation in standard form, we can rearrange the slope-intercept form equation.
y = -5x + 60
Multiply both sides of the equation by -1 to eliminate the negative coefficient of x:
-y = 5x - 60
Add 5x to both sides:
5x + y = -60
Therefore, the equation in standard form is: 5x + y = -60.
wright this in slope intercept form
y=-5x+60
The equation y = -5x + 60 is already in slope-intercept form. This form is y = mx + b, where m is the slope (-5 in this case) and b is the y-intercept (60 in this case).
now wright it in standard form
To write the equation y = -5x + 60 in standard form, we need to move all the variables to the same side of the equation and put the coefficients of x and y in front of them.
Starting with the equation y = -5x + 60:
Rearranging it, we get:
5x + y = 60
So the equation in standard form is 5x + y = 60.
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 rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point) Responses (y+10)=−5(x−10) open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren (y−45)=−5(x−3) open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren (y−3)=−5(x−45) open paren y minus 3 close paren is equal to negative 5 times open paren x minus 45 close paren (y−10)=−5(x+10)
Given the two points (3, 45) and (10, 10), we can use the point-slope formula to find the equation.
The general point-slope formula is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Using the first point (3, 45), we have:
y - 45 = m(x - 3)
To find the slope (m), we can use the second point (10, 10):
m = (y2 - y1)/(x2 - x1) = (10 - 45)/(10 - 3) = -35/7 = -5
Substituting the value of m into the equation, we get:
y - 45 = -5(x - 3)
The equation in point-slope form, using the given points, is:
(y - 45) = -5(x - 3)
The tables below show the number of jumping jacks completed after a given period of time in seconds. Kimberly: Time (seconds) Jumping Jacks 3 17 8 37 12 53 16 69 Katrina: Time (seconds) Jumping Jacks 2 10 5 25 12 60 20 100(3 points) a. Which person is doing more jumping jacks per second? b. Which person had done more jumping jacks initially before the timer started? c. Which person shows a proportional relationship?
a. To find the rate of change (slope) for this scenario, you can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 60 - 10 = 50 feet, and the change in x is 10 - 3 = 7 days. Plugging these values into the formula:
slope = 50 / 7
b. The y-intercept represents the starting point of the scenario, which is the water level of the river before the drought began. In this case, the y-intercept is given as 60 feet.
c. To write the equation for the scenario in slope-intercept form (y = mx + b), you can substitute the values:
y = (50/7)x + 60
d. To write the equation in standard form (Ax + By = C), you need to rearrange the equation:
7y = 50x + 420
-50x + 7y = 420