13Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rainThe river was 60 feet before the drought began (points)
a What is the rate of change slopefor this scenario?
bWhat is the y-intercept for this scenario?
cWhite an equation for the scenario in slope-intercept form
d White an equation in standard form
-5x+y=60
5
y=5x+45
y=-5x+60
-5
5x+y=60
y=-5x-35
15
5x+y=35
(0,60)
(0,-5)
(-5,0)
a) The rate of change (slope) for this scenario can be calculated by finding the change in y (water level) divided by the change in x (number of days):
Slope = (45 - 10) / (3 - 10) = -35 / -7 = 5
b) The y-intercept for this scenario is the initial water level before the drought began. In this case, the river was 60 feet before the drought began. So, the y-intercept is 60.
c) The equation for the scenario in slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.
So, the equation is: y = 5x + 60.
d) The equation in standard form is ax + by = c. Rearranging the equation from part c, we get:
y = 5x + 60
-5x + y = 60
-5x + y - 60 = 0
So, the equation in standard form is: -5x + y - 60 = 0.
a) To find the rate of change (slope) in this scenario, we need to calculate the change in y (water level) divided by the change in x (number of days).
Change in y = Final water level - Initial water level = 10 ft - 60 ft = -50 ft (since the water level decreased)
Change in x = Final number of days - Initial number of days = 10 days - 0 days = 10 days
Slope = Change in y / Change in x = -50 ft / 10 days = -5 ft/day
b) The y-intercept is the point where the line intersects the y-axis. In this scenario, the y-intercept is the initial water level before the drought began, which is 60 feet.
c) The slope-intercept form of an equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Therefore, for this scenario, the equation in slope-intercept form would be:
y = -5x + 60
d) The standard form of an equation is given by Ax + By = C, where A, B, and C are constants.
To convert the equation y = -5x + 60 to standard form, we need to eliminate the decimal slope (-5) by multiplying both sides of the equation by 5:
5y = -5(5x) + 5(60)
5y = -25x + 300
Now, rearrange the equation so that the x and y terms are on the same side:
25x + 5y = 300
The equation in standard form is: 25x + 5y = 300.
To find the rate of change (slope) in this scenario, we can use the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
From the information given, the water level decreased from 60 feet to 10 feet over a period of 10 days. So, the change in y-coordinate is 10 - 60 = -50, and the change in x-coordinate is 10 - 0 = 10.
Therefore, the slope is:
slope = (-50) / 10 = -5
The y-intercept is the y-coordinate when the x-coordinate is 0. From the scenario, the water level was 60 feet before the drought began, which corresponds to the point (0, 60). So the y-intercept is 60.
Now we can write the equation for this scenario in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The equation is:
y = -5x + 60
To write the equation in standard form, we move the variables to one side and rewrite the equation as:
5x + y = 60
So, the equation in standard form is:
5x + y = 60