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 rain. The river was 60 feet before the drought began.(4 points)%0D%0APut 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.%0D%0Aa. What is the rate of change (slope) for this scenario? Response area%0D%0A%0D%0Ab. What is the y-intercept for this scenario? Response area%0D%0A%0D%0Ac. Write an equation for the scenario in slope-intercept form. Response area%0D%0A%0D%0Ad. Write an equation in standard form.
15
-5
5x=y=60
(0,-5)
5x+y=35
(-5,0)
-5x=y=60
y=-5x-35
y=5x+45
y=-5x+60
5
(0,60)
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.
wrong fix it please
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. The rate of change (slope) for this scenario can be calculated using the formula:
Slope = (change in y) / (change in x)
In this case, the change in y is 10 - 45 = -35 and the change in x is 10 - 3 = 7.
So the slope is -35 / 7 = -5.
b. The y-intercept for this scenario is the value of y when x is 0. From the given information, we know that the river was 60 feet before the drought began. Therefore, the y-intercept is 60.
c. To write an equation for the scenario in slope-intercept form (y = mx + b), we can use the values of the slope (-5) and the y-intercept (60).
So the equation in slope-intercept form is: y = -5x + 60.
d. To write an equation in standard form (Ax + By = C), we can rearrange the slope-intercept form equation.
Starting with the slope-intercept form equation: y = -5x + 60
Multiply both sides by -1 to make the coefficient of x positive: -y = 5x - 60
Rearrange terms: 5x + y = -60
Therefore, the equation in standard form is: 5x + y = -60.
To find the rate of change (slope) for this scenario, we can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 10 feet (from 60 feet to 10 feet), and the change in x is 10 days (from 0 days to 10 days).
slope = (10 feet) / (10 days) = 1 foot/day
Therefore, the rate of change (slope) for this scenario is 1 foot/day.
To find the y-intercept, we can use the point-slope form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
From the given data, we know that after 3 days of no rain, the water level is 45 feet. So we can use this point (3, 45) to find the y-intercept.
45 = 1(3) + b
45 = 3 + b
b = 45 - 3
b = 42
Therefore, the y-intercept for this scenario is 42.
Now, let's write the equation for the scenario in slope-intercept form: y = mx + b.
Using the slope (m = 1) and the y-intercept (b = 42), we can write:
y = 1x + 42
Simplifying it, the equation in slope-intercept form is:
y = x + 42
To write the equation in standard form, we need to rearrange the equation and put it in the form Ax + By = C.
y = x + 42
Rearranging: -x + y = 42
Multiplying by -1 to get the coefficient of x positive: x - y = -42
Therefore, the equation in standard form is:
x - y = -42