Question

The linear equation represented on the coordinate plane shows the average temperature increase in a city since the year 2000



Select all the statements that are true for the linear equation.

(3 points)
Responses

y = 0.2x + 15 represents the linear equation
y = 0.2x + 15 represents the linear equation

The average increase in temperature each year is 1°C.
The average increase in temperature each year is 1°C.

In the year 2010 the temperature was 17 ° C.
In the year 2010 the temperature was 17 ° C.

If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029
If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029

The average increase in temperature every 5 years is 1°C.
The average increase in temperature every 5 years is 1°C.
Question 2
2.

Which equations have the solution set of {14, −5}
?

Select all that apply.

(3 points)
Responses

(4x − 1)(x+5)=0
(4x − 1)(x+5)=0

(x − 14)(x − 5) = 0
(x − 14)(x − 5) = 0

(2x - 8)(x - 5) = 0
(2x - 8)(x - 5) = 0

(x + 14)(x + 5) = 0
(x + 14)(x + 5) = 0

(8x - 2)(x + 5) = 0
(8x - 2)(x + 5) = 0

(4x + 2)(x + 5) = 0
(4x + 2)(x + 5) = 0

(x − 14)(x + 5) = 0
(x − 14)(x + 5) = 0
Question 3
3.

The graph of the equation f(x) = x2 − 5x + 6
is shown on the coordinate plane.



Complete the statements

(2 points)
The solutions to the equation f(x) = x2 − 5x + 6
when f(x) = 6 are the points

The solutions to the equation f(x) = x2 − 5x + 6
when f(2) and f(3) are the points


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Answer 1

Let's address each question one by one:

### Question 1:
The linear equation is given as **y = 0.2x + 15**.

1. **True:** The linear equation is correctly represented as **y = 0.2x + 15**.
2. **False:** The average increase in temperature each year is **0.2°C**, not **1°C** (this is the slope of the line).
3. **True:** In the year 2010 (which is x=10), the temperature would be:
\[ y = 0.2(10) + 15 = 2 + 15 = 17°C. \]
4. **True:** If the trend continues, since the slope is 0.2°C per year, the temperature in 2030 (which is x=30) will be:
\[ y = 0.2(30) + 15 = 6 + 15 = 21°C. \]
The temperature in 2029 (x=29) will be:
\[ y = 0.2(29) + 15 = 5.8 + 15 = 20.8°C. \]
Thus, the temperature in 2030 will be \( 21°C \), which is \( 0.2°C \) higher than in 2029 but not 1°C higher. So this statement is **False**.
5. **False:** The average increase in temperature every 5 years is:
\[ 0.2°C/year \times 5 years = 1°C. \]
Therefore, this statement is **True**.

**True statements from Question 1:**
- y = 0.2x + 15 represents the linear equation.
- In the year 2010 the temperature was 17°C.
- The average increase in temperature every 5 years is 1°C.

### Question 2:
We need to find equations that have the solution set of {14, -5}.

1. **True:** \((4x - 1)(x + 5) = 0\) gives \(x = \frac{1}{4}\) and \(x = -5\).
2. **False:** \((x - 14)(x - 5) = 0\) gives \(x = 14\) and \(x = 5\).
3. **False:** \((2x - 8)(x - 5) = 0\) gives \(x = 4\) and \(x = 5\).
4. **False:** \((x + 14)(x + 5) = 0\) gives \(x = -14\) and \(x = -5\).
5. **False:** \((8x - 2)(x + 5) = 0\) gives \(x = \frac{1}{4}\) and \(x = -5\).
6. **False:** \((4x + 2)(x + 5) = 0\) gives \(x = -\frac{1}{2}\) and \(x = -5\).
7. **True:** \((x - 14)(x + 5) = 0\) gives \(x = 14\) and \(x = -5\).

**Equations with the solution set of {14, -5}:**
- \((4x - 1)(x + 5) = 0\)
- \((x - 14)(x + 5) = 0\)

### Question 3:
The equation is \(f(x) = x^2 - 5x + 6\).

- The solutions to the equation \(f(x) = x^2 - 5x + 6\) when \(f(x) = 6\) are the points where the graph intersects the line \(y=6\). This occurs at the points corresponding to the roots of the equation, which can be calculated by setting \(f(x) = 6\):
\[
x^2 - 5x + 6 - 6 = 0 \Rightarrow x^2 - 5x = 0 \Rightarrow x(x - 5) = 0 \Rightarrow x = 0, 5.
\]

- The solutions to the equation \(f(x) = x^2 - 5x + 6\) when \(f(2)\) and \(f(3)\) correspond to the output of the function at these inputs:
- \(f(2) = 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0.\)
- \(f(3) = 3^2 - 5(3) + 6 = 9 - 15 + 6 = 0.\)

Thus, the points when \(f(x) = 0\) occur at \( x=2, 3\).

**Points for completion about \( f(x) = x^2 - 5x + 6 \):**
1. When \(f(x) = 6\) → the points are (0, 6) and (5, 6).
2. When \(f(2)\) and \(f(3)\) → the points are (2, 0) and (3, 0).

I hope this clarifies the questions and provides accurate responses!