Change the equation from standard to slope-intercept form by solving for y
11x-8y=-48
Bobs work:
-8y=-59x
Y=7.375
Bills work:
-8y=-11x-48
Y=11/8x+6
Buds work:
-8y= -11x-48
Y=-11x+6
Who solved for y correctly?
A. None of them are correct
B. Bob
C. Bill
D. Bud
D. Bud
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 the scenario in slope-intercept form.
D. Write this equation in standard form.
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 62 - 22 = 40 feet (from 22 feet to 62 feet), and the change in x is 10 - 0 = 10 days (from 0 days of rain to 10 days of rain). Therefore, the slope is:
slope = 40 / 10 = 4 feet per day
So, the rate of change (slope) for this scenario is 4 feet per day.
The y-intercept is the value of y when x is 0. In this scenario, when there are 0 days of rain, the water level is 22 feet. Therefore, the y-intercept is 22.
So, the y-intercept for this scenario is 22.
To write the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we have:
y = 4x + 22
Therefore, the equation for the scenario in slope-intercept form is y = 4x + 22.
To write this equation in standard form (Ax + By = C), we can rearrange it as:
-4x + y = 22
Therefore, the equation in standard form is -4x + y = 22.
The correct answer is:
D. Bud
Bud solved for y correctly by rearranging the original equation to isolate y as:
Y = -11x + 6
To change the equation from standard form to slope-intercept form (y = mx + b), we need to solve the equation for y.
Let's go through the options one by one and check if their solutions are correct.
Option A (None of them are correct):
-8y = -59x
Dividing both sides by -8:
y = 59/8x
The solution is not correct because it should be y = mx + b, and there is no constant term (b) in the equation.
Option B (Bob):
-8y = -11x - 48
Dividing both sides by -8:
y = 11/8x + 6
The solution provided is correct. It is in the slope-intercept form (y = mx + b) and has the correct slope (m) and y-intercept (b).
Option C (Bill):
-8y = -11x - 48
Dividing both sides by -8:
y = 11/8x + 6
The solution provided is correct. It is in the slope-intercept form (y = mx + b) and has the correct slope (m) and y-intercept (b).
Option D (Bud):
-8y = -11x - 48
Dividing both sides by -8:
y = 11/8x + 6
The solution provided is not correct. It is the same as option C, which means there was an error in Bud's work.
Therefore, the correct answers are B (Bob) and C (Bill). They both solved for y correctly and provided the equation in slope-intercept form as required.
Note: It is always a good practice to double-check your work and ensure the equation is in the correct form.