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11. Change the equation from standard form to slope-intercept form by solving for y.

11x−8y=−48
Bob's work:

−8y=−59x
y=7.375
Bill's work:

−8y=−11x−48
y=118x+6
Bud's work:

−8y=−11x−48
y=−11x+6
Who solved for y correctly?

(1 point)
Responses

Bob
Bob

Bud
Bud

Bill
Bill

None of them are correct
None of them are correct
Question 2
12. 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.(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 this equation in standard form. Response area

Question 3
13. 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?

(1 point)
Responses

(y - 10) = 4 (x + 62)
(y - 10) = 4 (x + 62)

(y - 34) = 4 (x - 3)
(y - 34) = 4 (x - 3)

(y - 34) = 4 (x - 10)
(y - 34) = 4 (x - 10)

(y - 3) = 4 (x - 34)
(y - 3) = 4 (x - 34)
Question 4
14. Which graph matches the linear equation: 6x+y=−4
(1 point)
Responses

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1 answer

Let's go through your questions one by one.

Question 1: Change the equation from standard form to slope-intercept form

You are given the equation: \[ 11x - 8y = -48 \]

Let's solve for \(y\).

  1. Isolate \(y\): \[ -8y = -11x - 48 \]
  2. Divide everything by -8: \[ y = \frac{11}{8}x + 6 \]

Now compare this to the work of Bob, Bill, and Bud:

  • Bob's Work: Incorrect, as he miscalculated during his steps.
  • Bill's Work: Incorrect due to a miscalculation in determining the coefficients.
  • Bud's Work: Incorrect because he miscalculated the sign of the slope.

Conclusion for Question 1:

None of them are correct.

Question 2: Rate of Change, y-Intercept, and Equations

Given data:

  • Before the rain, the river was 22 feet.
  • After 3 days, it was 34 feet.
  • After 10 days, it was 62 feet.

We take the points \( (3, 34) \) and \( (10, 62) \).

a. Rate of Change (slope): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4 \]

b. y-intercept: To find the y-intercept, we'll use the point-slope form. The initial reading was 22 before it started to rain. This translates to: The y-intercept \(b\) can be calculated using \(y = mx + b\). Using the point \( (0, 22) \): \[ y = 4x + 22 \] The y-intercept is 22.

c. Equation in slope-intercept form: From above, the equation is: \[ y = 4x + 22 \]

d. Equation in standard form: To convert \(y = 4x + 22\) to standard form, rearranging gives: \[ -4x + y = 22 \] We can multiply through by -1: \[ 4x - y = -22 \]

Question 3: Point-Slope Equation

Given Points: \( (3, 34) \) and \( (10, 62) \)

Using point-slope form: \[ y - y_1 = m(x - x_1) \] Where \(m = 4\) and we can use the point \( (3, 34) \): \[ y - 34 = 4(x - 3) \]

Conclusion for Question 3:

(y - 34) = 4 (x - 3)

Question 4: Graph matching the linear equation \( 6x + y = -4 \)

Rearranging to slope-intercept form:

\[ y = -6x - 4 \] This indicates that the slope is \(-6\) and the y-intercept is \(-4\). You would need to look for a graph that has these characteristics.

If you have graphs to compare, look for one that shows a line decreasing steeply with a y-intercept at -4.

Let me know if you need further assistance or clarification on any of the points!