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 )
12. graph using slope intercept form. ( y = -\frac{2}{3}x + 4 )
13. graph using x and y intercepts. ( 2x + 3y = 6 )
14. graph using x and y intercepts. ( x - y = 4 )
15. the bird flu is attacking eagletown. the function ( b(t) = 9t - 4 ) models the number of people who have bird flu where ( t = ) time (in days) and ( b = ) 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 )
12. graph using slope intercept form. ( y = -\frac{2}{3}x + 4 )
13. graph using x and y intercepts. ( 2x + 3y = 6 )
14. graph using x and y intercepts. ( x - y = 4 )
15. the bird flu is attacking eagletown. the function ( b(t) = 9t - 4 ) models the number of people who have bird flu where ( t = ) time (in days) and ( b = ) 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 (Graphing $y=-2x + 6$ using slope - intercept form)
# Explanation:
## Step1: Identify slope and y - intercept
The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the line $y=-2x+6$, the slope $m=-2$ and the y - intercept $b = 6$ (so the point $(0,6)$ is on the line).
## Step2: Use slope to find another point
The slope $m=\frac{\text{rise}}{\text{run}}=-2=\frac{-2}{1}$. Starting from the y - intercept $(0,6)$, we move down 2 units (because rise is - 2) and 1 unit to the right (run is 1) to get the point $(1,4)$. We can also move up 2 units and 1 unit to the left to get $(-1,8)$. Then we draw a line through these points.
# Answer:
Slope: $-2$, y - intercept: $6$ (the line passes through $(0,6)$ and other points found using the slope, e.g., $(1,4)$).

### Problem 12 (Graphing $y =-\frac{2}{3}x + 4$ using slope - intercept form)
# Explanation:
## Step1: Identify slope and y - intercept
For the line $y=-\frac{2}{3}x + 4$, the slope $m =-\frac{2}{3}$ and the y - intercept $b = 4$ (so the point $(0,4)$ is on the line).
## Step2: Use slope to find another point
The slope $m=\frac{\text{rise}}{\text{run}}=-\frac{2}{3}$. Starting from the y - intercept $(0,4)$, we move down 2 units (rise=-2) and 3 units to the right (run = 3) to get the point $(3,2)$. We can also move up 2 units and 3 units to the left to get $(-3,6)$. Then we draw a line through these points.
# Answer:
Slope: $-\frac{2}{3}$, y - intercept: $4$ (the line passes through $(0,4)$ and other points found using the slope, e.g., $(3,2)$).

### Problem 13 (Graphing $2x + 3y=6$ using x and y intercepts)
# Explanation:
## Step1: Find x - intercept
To find the x - intercept, we set $y = 0$ in the equation $2x+3y = 6$. Then $2x+3(0)=6$, which simplifies to $2x=6$. Solving for $x$, we get $x = 3$. So the x - intercept is $(3,0)$.
## Step2: Find y - intercept
To find the y - intercept, we set $x = 0$ in the equation $2x+3y = 6$. Then $2(0)+3y=6$, which simplifies to $3y=6$. Solving for $y$, we get $y = 2$. So the y - intercept is $(0,2)$.
## Step3: Graph the line
We plot the points $(3,0)$ and $(0,2)$ and draw a line through them.
# Answer:
x - intercept: $(3,0)$, y - intercept: $(0,2)$ (the line passes through these two points).

### Problem 14 (Graphing $x - y=4$ using x and y intercepts)
# Explanation:
## Step1: Find x - intercept
To find the x - intercept, we set $y = 0$ in the equation $x - y=4$. Then $x-0 = 4$, so $x = 4$. The x - intercept is $(4,0)$.
## Step2: Find y - intercept
To find the y - intercept, we set $x = 0$ in the equation $x - y=4$. Then $0 - y=4$, which simplifies to $y=-4$. The y - intercept is $(0,-4)$.
## Step3: Graph the line
We plot the points $(4,0)$ and $(0,-4)$ and draw a line through them.
# Answer:
x - intercept: $(4,0)$, y - intercept: $(0,-4)$ (the line passes through these two points).

### Problem 15A (Finding $B(4)$ for $B(t)=9t - 4$)
# Explanation:
## Step1: Substitute $t = 4$ into the function
We have the function $B(t)=9t - 4$. To find $B(4)$, we substitute $t = 4$ into the function: $B(4)=9(4)-4$.
## Step2: Calculate the value
First, calculate $9(4)=36$. Then $B(4)=36 - 4=32$. In the context of the problem, $t$ is time in days and $B(t)$ is the number of sick people in thousands. So $B(4) = 32$ means that after 4 days, 32,000 people in Eagletown have bird flu.
# Answer:
$B(4)=32$. It means after 4 days, 32,000 people in Eagletown have bird flu.

### Problem 15B (Finding $t$ when $B(t)=23$ for $B(t)=9t - 4$)
# Explanation:
## Step1: Set up the equation
We set $B(t)=23$ in the function $B(t)=9t - 4$, so we have the equation $9t-4 = 23$.
## Step2: Solve for $t$
First, add 4 to both sides of the equation: $9t-4 + 4=23 + 4$, which simplifies to $9t=27$. Then divide both sides by 9: $t=\frac{27}{9}=3$. In the context of the problem, $t = 3$ means that after 3 days, 23,000 people in Eagletown have bird flu.
# Answer:
$t = 3$. It means after 3 days, 23,000 people in Eagletown have bird flu.

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: Use slope to find another point

Answer:

Problem 10