3. 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)

Question

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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 an equation in standard form. Response area

Question 2
14. 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. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point)
Responses

(y−45)=−5(x−3)
open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren

(y−10)=−5(x+10)
open paren y minus 10 close paren is equal to negative 5 times open paren x plus 10 close paren

(y−3)=−5(x−45)
open paren y minus 3 close paren is equal to negative 5 times open paren x minus 45 close paren

(y+10)=−5(x−10)
open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren
Question 3
15. Which graph matches the linear equation: −2x+3y=−6
(1 point)
Responses

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Answer 1

Let's go through each part of the problem step by step.

Part a: What is the rate of change (slope) for this scenario?

To find the slope (rate of change), we can use the formula for the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Given the two points:

• \( (3, 45) \) and \( (10, 10) \)
• Here, \( (x_1, y_1) = (3, 45) \) and \( (x_2, y_2) = (10, 10) \)

Calculating the slope: \[ m = \frac{10 - 45}{10 - 3} = \frac{-35}{7} = -5 \]

Rate of change (slope): -5

Part b: What is the y-intercept for this scenario?

The initial water level before the drought is 60 feet, which indicates the y-intercept (where \(x=0\)): Y-intercept: 60

Part c: Write an equation for the scenario in slope-intercept form.

Using the slope-intercept form \(y = mx + b\):

• Slope \(m = -5\)
• Y-intercept \(b = 60\)

Thus, the equation is: \[ y = -5x + 60 \]

Part d: Write an equation in standard form.

Standard form is \(Ax + By = C\).

Starting with the slope-intercept form: \[ y = -5x + 60 \]

Rearranging to standard form: \[ 5x + y = 60 \]

Question 2: Write the point-slope equation.

From the point (3, 45) with a slope of -5: Using the point-slope form \(y - y_1 = m(x - x_1)\): \[ y - 45 = -5(x - 3) \]

So the correct response is: (y−45)=−5(x−3)

Question 3: Which graph matches the linear equation: −2x + 3y = −6?

To convert \(-2x + 3y = -6\) to slope-intercept form:

1. Add \(2x\) to both sides: \[ 3y = 2x - 6 \]

2. Divide everything by 3 to isolate \(y\): \[ y = \frac{2}{3}x - 2 \]

From this, we can deduce the slope is \(\frac{2}{3}\) and the y-intercept is -2.

Look for a graph that has a y-intercept at -2 and a slope of \(\frac{2}{3}\).

Now you can arrange the responses based on the explanations provided.