9. write an equation in any form to represent the table.
|x|y|
|0|8|
|2|12|
|4|16|
|6|20|
10. the weekly revenue for monster mini golf for x golfers is given by the function r(x). explain the meaning of r(142).
11. evaluate the expression mx + b if m = 3/4, x = 20 and b=-6.
12. write an equation for the graph.
13. the third and fifth terms of an arithmetic sequence are a3 = 20 and a5 = 4. find the common difference d and a1.
14. write the equation of a line in point - slope form if the slope is 10 and a point on the line is (4, - 5).
15. which equations represent the graphed line? select all that apply.
a. y - 1 = 0.25(x + 4)
b. x - 4y=-8
c. y - 4 = 0.25(x - 3)
d. y = 1/4x + 2
e. x = 4y - 8
f. y = 0.25(x + 8)
g. y + 3 = 0.25(x + 4)

Question

Accepted Answer

### 9.
# Explanation:
## Step1: Find the slope
The slope $m$ between two - points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,8)$ and $(2,12)$: $m=\frac{12 - 8}{2 - 0}=\frac{4}{2}=2$. The $y$ - intercept $b$ is the value of $y$ when $x = 0$, so $b = 8$. The equation of the line in slope - intercept form is $y=mx + b$, so $y = 2x+8$.
# Answer:
$y = 2x + 8$

### 10.
# Explanation:
The function $R(x)$ represents the weekly revenue for Monster Mini Golf for $x$ golfers. When $x = 142$, $R(142)$ represents the weekly revenue for Monster Mini Golf when there are 142 golfers.
# Answer:
The weekly revenue for Monster Mini Golf when there are 142 golfers.

### 11.
# Explanation:
## Step1: Substitute values
Substitute $m=\frac{3}{4}$, $x = 20$, and $b=-6$ into the expression $mx + b$. We get $\frac{3}{4}	imes20-6$.
## Step2: Calculate
$\frac{3}{4}	imes20=15$, then $15-6 = 9$.
# Answer:
$9$

### 12. (Since no points on the graph are given precisely, assume we can find two points $(x_1,y_1)$ and $(x_2,y_2)$ to get the slope and $y$ - intercept)
# Explanation:
Let's assume two points on the line to find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ and then use the slope - intercept form $y=mx + b$ (find $b$ by substituting one of the points). But without specific points, we can't give a numerical answer. If we assume the line passes through $(0,2)$ and $(4,3)$:
## Step1: Calculate slope
$m=\frac{3 - 2}{4 - 0}=\frac{1}{4}=0.25$. The $y$ - intercept $b = 2$. The equation is $y=0.25x + 2$.
# Answer:
$y = 0.25x+2$ (assuming points $(0,2)$ and $(4,3)$)

### 13.
# Explanation:
## Step1: Use the formula for the $n$th term of an arithmetic sequence
The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. We know that $a_3=a_1+2d = 20$ and $a_5=a_1+4d = 4$.
## Step2: Subtract the first equation from the second
$(a_1 + 4d)-(a_1+2d)=4 - 20$. This simplifies to $2d=-16$, so $d=-8$.
## Step3: Find $a_1$
Substitute $d=-8$ into $a_1+2d = 20$. We get $a_1+2	imes(-8)=20$, so $a_1=20 + 16=36$.
# Answer:
$d=-8$, $a_1 = 36$

### 14.
# Explanation:
The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Given $m = 10$ and the point $(4,-5)$, we substitute these values into the formula.
# Answer:
$y+5 = 10(x - 4)$

### 15.
# Explanation:
First, find the slope of the line from the graph. Let's assume two points on the line, say $(-4,1)$ and $(0,2)$. The slope $m=\frac{2 - 1}{0+4}=\frac{1}{4}=0.25$.
## Step1: Check each equation
- For $A$: $y - 1=0.25(x + 4)$ can be rewritten as $y=0.25x+2$, which is correct.
- For $B$: $x-4y=-8$ can be rewritten as $y=\frac{1}{4}x + 2$, which is correct.
- For $C$: $y - 4=0.25(x - 3)$ gives $y=0.25x+3.25$, which is incorrect.
- For $D$: $y=\frac{1}{4}x + 2$, which is correct.
- For $E$: $x = 4y-8$ can be rewritten as $y=\frac{1}{4}x + 2$, which is correct.
- For $F$: $y=0.25(x + 8)=0.25x+2$, which is correct.
- For $G$: $y + 3=0.25(x + 4)$ gives $y=0.25x - 2$, which is incorrect.
# Answer:
A. $y - 1=0.25(x + 4)$, B. $x - 4y=-8$, D. $y=\frac{1}{4}x + 2$, E. $x = 4y-8$, F. $y=0.25(x + 8)$

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QUESTION IMAGE

Question

Explanation:

9.

Step1: Find the slope

Step1: Substitute values

Step2: Calculate

Answer:

10.