Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.
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 this scenario in slope intercept form.
D. write this equation in standard form.
To find the rate of change (slope) for this scenario, we need to determine the change in the water level divided by the change in the number of days.
The change in the water level is 62 feet - 34 feet = 28 feet.
The change in the number of days is 10 days - 3 days = 7 days.
Therefore, the rate of change (slope) is 28 feet / 7 days = 4 feet per day (ft/day).
The y-intercept represents the initial water level before the rain began, which is given as 22 feet.
Therefore, the y-intercept for this scenario is 22 feet.
To write an equation for this scenario in slope-intercept form (y = mx + b), we can use the values we have determined: the slope (m) and the y-intercept (b).
The equation is: y = 4x + 22.
To write this equation in standard form (Ax + By = C), we need to rearrange the equation:
y = 4x + 22
-4x + y = 22
-4x + y - 22 = 0
Therefore, the equation in standard form is: -4x + y - 22 = 0.
What is the rate of change (slope) for this scenario?
The rate of change (slope) for this scenario is 4 feet per day (ft/day).
Write this equation in standard form
To write the equation in standard form, we need to rearrange it so that it follows the format Ax + By = C.
The slope-intercept form of the equation is y = 4x + 22.
To convert this equation to standard form, we need to eliminate the fraction. We can achieve this by multiplying all the terms by a common denominator, which is 1 in this case.
Multiplying each term by 1, we get:
1(y) = 1(4x) + 1(22)
Which simplifies to:
y = 4x + 22
Now, we need to move the x term to the left side and rewrite the equation:
-4x + y = -4x + 4x + 22
Combining like terms, we have:
-4x + y = 22
Rearranging it further, we have:
-4x + y -22 = 0
Therefore, the equation in standard form is: -4x + y - 22 = 0.
Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.
Given the two points we know: (3,34) and (10,62), what would the point-slope equation look like?
A. (y-34)=4(x-3)
B. (y-34=4(x-10)
C. (y-3)=4(x-34)
D. (y-10)=4(x+62)
To find the point-slope equation, we need to use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope.
Given the two points (3,34) and (10,62), we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (62 - 34) / (10 - 3)
m = 28 / 7
m = 4
Now, we can choose one of the points and plug it into the equation:
Using the point (3,34):
y - 34 = 4(x - 3)
Therefore, the correct point-slope equation is:
A. (y-34)=4(x-3)