9. the function g is a linear function. the y-intercept of the graph of ( y = g(x) ) in the xy-plane is ( (0, -3) ). what is the y-intercept of the graph of ( y = g(x) + 5 )?
10. the function h is a linear function. the y-intercept of the graph of ( y = h(x) ) in the xy-plane is ( (0, 8) ). what is the y-intercept of the graph of ( y = h(x) - 12 )?
11. graph using slope intercept form. ( y = -2x + 6 )
slope:
y-intercept:
coordinate plane image
12. graph using slope intercept form. ( y = -\frac{2}{3}x + 4 )
slope:
y-intercept:
coordinate plane image
13. graph using x and y intercepts. ( 2x + 3y = 6 )
x-intercept:
y-intercept:
coordinate plane image
14. graph using x and y intercepts. ( x - y = 4 )
x-intercept:
y-intercept:
coordinate plane image
15. the bird flu is attacking eagletown. the function ( b(t) = 9t - 4 ) models the number of people who have bird flu where ( t = ext{time (in days)} ) and ( b = ext{the number of sick people (in thousands)}. )
a. find ( s(4) ) and explain what it means in the context of the problem.
b. find ( t ) when ( b(t) = 23 ) and explain what it means in the context of the problem.

Question

9. the function g is a linear function. the y-intercept of the graph of ( y = g(x) ) in the xy-plane is ( (0, -3) ). what is the y-intercept of the graph of ( y = g(x) + 5 )?
10. the function h is a linear function. the y-intercept of the graph of ( y = h(x) ) in the xy-plane is ( (0, 8) ). what is the y-intercept of the graph of ( y = h(x) - 12 )?
11. graph using slope intercept form. ( y = -2x + 6 )
    slope:
    y-intercept:
    coordinate plane image
12. graph using slope intercept form. ( y = -\frac{2}{3}x + 4 )
    slope:
    y-intercept:
    coordinate plane image
13. graph using x and y intercepts. ( 2x + 3y = 6 )
    x-intercept:
    y-intercept:
    coordinate plane image
14. graph using x and y intercepts. ( x - y = 4 )
    x-intercept:
    y-intercept:
    coordinate plane image
15. the bird flu is attacking eagletown. the function ( b(t) = 9t - 4 ) models the number of people who have bird flu where ( t = 	ext{time (in days)} ) and ( b = 	ext{the number of sick people (in thousands)}. )
    a. find ( s(4) ) and explain what it means in the context of the problem.
    b. find ( t ) when ( b(t) = 23 ) and explain what it means in the context of the problem.

Accepted Answer

### Problem 9
# Explanation:
## Step1: Recall y - intercept definition
The y - intercept of a function $y = g(x)$ is the value of $y$ when $x = 0$. Given the y - intercept of $y=g(x)$ is $(0,-3)$, so $g(0)=-3$.

## Step2: Find y - intercept of $y = g(x)+5$
To find the y - intercept of $y = g(x)+5$, we set $x = 0$. Then $y=g(0)+5$. Substitute $g(0)=-3$ into the equation: $y=-3 + 5=2$.

# Answer:
The y - intercept of the graph of $y = g(x)+5$ is $2$.

### Problem 10
# Explanation:
## Step1: Recall y - intercept definition
The y - intercept of a function $y = h(x)$ is the value of $y$ when $x = 0$. Given the y - intercept of $y = h(x)$ is $(0,8)$, so $h(0)=8$.

## Step2: Find y - intercept of $y=h(x)-12$
To find the y - intercept of $y=h(x)-12$, we set $x = 0$. Then $y=h(0)-12$. Substitute $h(0) = 8$ into the equation: $y=8-12=-4$.

# Answer:
The y - intercept of the graph of $y=h(x)-12$ is $-4$.

### Problem 11
# Explanation:
The slope - intercept form of a linear equation is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

## Step1: Identify slope and y - intercept
For the equation $y=-2x + 6$, comparing with $y=mx + b$, we have $m=-2$ (slope) and $b = 6$ (y - intercept).

## Step2: Graphing (brief description)
- Plot the y - intercept $(0,6)$ on the y - axis.
- The slope $m=-2=\frac{-2}{1}$, so from the y - intercept, move down 2 units and right 1 unit (or up 2 units and left 1 unit) to get another point. Then draw a line through the two points.

# Answer:
Slope: $-2$
y - intercept: $6$

### Problem 12
# Explanation:
The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

## Step1: Identify slope and y - intercept
For the equation $y=-\frac{2}{3}x + 4$, comparing with $y=mx + b$, we have $m =-\frac{2}{3}$ (slope) and $b = 4$ (y - intercept).

## Step2: Graphing (brief description)
- Plot the y - intercept $(0,4)$ on the y - axis.
- The slope $m=-\frac{2}{3}=\frac{-2}{3}$, so from the y - intercept, move down 2 units and right 3 units (or up 2 units and left 3 units) to get another point. Then draw a line through the two points.

# Answer:
Slope: $-\frac{2}{3}$
y - intercept: $4$

### Problem 13
# Explanation:
To find the x - intercept, set $y = 0$ in the equation $2x+3y = 6$. To find the y - intercept, set $x = 0$ in the equation $2x + 3y=6$.

## Step1: Find x - intercept
Set $y = 0$ in $2x+3y = 6$:
$2x+3(0)=6$
$2x=6$
$x = 3$
So the x - intercept is $(3,0)$.

## Step2: Find y - intercept
Set $x = 0$ in $2x+3y = 6$:
$2(0)+3y=6$
$3y=6$
$y = 2$
So the y - intercept is $(0,2)$.

## Step3: Graphing (brief description)
- Plot the x - intercept $(3,0)$ on the x - axis and the y - intercept $(0,2)$ on the y - axis. Then draw a line through these two points.

# Answer:
x - intercept: $3$ (or $(3,0)$)
y - intercept: $2$ (or $(0,2)$)

### Problem 14
# Explanation:
To find the x - intercept, set $y = 0$ in the equation $x - y=4$. To find the y - intercept, set $x = 0$ in the equation $x - y = 4$.

## Step1: Find x - intercept
Set $y = 0$ in $x - y=4$:
$x-0 = 4$
$x = 4$
So the x - intercept is $(4,0)$.

## Step2: Find y - intercept
Set $x = 0$ in $x - y=4$:
$0 - y=4$
$y=-4$
So the y - intercept is $(0,-4)$.

## Step3: Graphing (brief description)
- Plot the x - intercept $(4,0)$ on the x - axis and the y - intercept $(0,-4)$ on the y - axis. Then draw a line through these two points.

# Answer:
x - intercept: $4$ (or $(4,0)$)
y - intercept: $-4$ (or $(0,-4)$)

### Problem 15 (Part A)
# Explanation:
The function is $B(t)=9t - 4$ (assuming there is a typo and it should be $B(4)$ instead of $S(4)$).

## Step1: Substitute $t = 4$ into $B(t)$
$B(4)=9(4)-4$
$B(4)=36 - 4$
$B(4)=32$

## Step2: Interpret the result
Since $B(t)$ models the number of people (in thousands) who have bird flu at time $t$ (in days), $B(4) = 32$ means that after 4 days, the number of people who have bird flu in Eagletown is $32\times1000 = 32000$ people.

# Answer:
$B(4)=32$. It means that after 4 days, 32,000 people (since $B(t)$ is in thousands) have bird flu in Eagletown.

### Problem 15 (Part B)
# Explanation:
We are given $B(t)=23$ and we need to find $t$ from the equation $B(t)=9t - 4$.

## Step1: Set up the equation
$9t-4 = 23$

## Step2: Solve for $t$
Add 4 to both sides: $9t=23 + 4=27$
Divide both sides by 9: $t=\frac{27}{9}=3$

## Step3: Interpret the result
Since $B(t)$ models the number of people (in thousands) who have bird flu at time $t$ (in days), $t = 3$ means that after 3 days, the number of people who have bird flu in Eagletown is 23,000 (since $B(t) = 23$ and $B(t)$ is in thousands).

# Answer:
$t = 3$. It means that after 3 days, 23,000 people have bird flu in Eagletown.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 9

Step1: Recall y - intercept definition

Step2: Find y - intercept of \(y = g(x)+5\)

Step1: Recall y - intercept definition

Step2: Find y - intercept of \(y=h(x)-12\)

Step1: Identify slope and y - intercept

Step2: Graphing (brief description)

Answer:

Problem 10