task 3: we are going to graph the following function without a table
$y = \frac{3}{5}x - 8$
e) what is the starting value of your
function?
f) where can your starting value be found
on your graph?
g) what is the rate of change of your
function?
h) use your rate of change to plot the whole
number points on your graph.

Question

Accepted Answer

### e)
# Explanation:
## Step1: Recall slope - intercept form
The slope - intercept form of a linear function is $y = mx + b$, where $b$ is the y - intercept (starting value when $x = 0$).
## Step2: Identify $b$ in the given function
For the function $y=\frac{3}{5}x - 8$, comparing with $y=mx + b$, we can see that $b=- 8$.
# Answer:
The starting value of the function is $-8$.

### f)
# Explanation:
## Step1: Recall the definition of y - intercept
The y - intercept (starting value) of a function $y = mx + b$ is the value of $y$ when $x = 0$.
## Step2: Determine the location on the graph
When $x = 0$, the point on the graph is $(0,b)$. For the function $y=\frac{3}{5}x - 8$, when $x = 0$, $y=-8$. So the starting value (y - intercept) is found at the point $(0,-8)$ on the y - axis.
# Answer:
The starting value can be found at the point $(0, - 8)$ on the y - axis.

### g)
# Explanation:
## Step1: Recall the slope - intercept form
The slope - intercept form of a linear function is $y=mx + b$, where $m$ is the slope (rate of change) of the function.
## Step2: Identify $m$ in the given function
For the function $y = \frac{3}{5}x-8$, comparing with $y = mx + b$, we can see that $m=\frac{3}{5}$.
# Answer:
The rate of change of the function is $\frac{3}{5}$.

### h)
# Explanation:
## Step1: Recall the slope (rate of change)
The slope of the function $y=\frac{3}{5}x - 8$ is $\frac{3}{5}$, which means for every increase of $5$ units in the $x$ - direction (run), the $y$ - value increases by $3$ units (rise), or for every increase of $1$ unit in $x$, $y$ increases by $\frac{3}{5}$ units.
## Step2: Start from the y - intercept
We know the y - intercept is $(0,-8)$. To find the next point, we use the slope. If we move $5$ units to the right (increase $x$ by $5$) from $x = 0$ to $x=5$, then we move $3$ units up (increase $y$ by $3$) from $y=-8$ to $y=-8 + 3=-5$. So the point is $(5,-5)$. If we move $5$ units to the left (decrease $x$ by $5$) from $x = 0$ to $x=-5$, then we move $3$ units down (decrease $y$ by $3$) from $y = - 8$ to $y=-8-3=-11$. So the point is $(-5,-11)$. We can also use the slope as a rise over run of $\frac{3}{5}$ (for $x$ increase by $1$, $y$ increases by $\frac{3}{5}$) to find other points. For example, when $x = 1$, $y=\frac{3}{5}(1)-8=\frac{3 - 40}{5}=-\frac{37}{5}=-7.4$ (not a whole number point), when $x = 5$, $y=-5$ (whole number point), when $x = 10$, $y=\frac{3}{5}(10)-8=6 - 8=-2$ (whole number point), when $x=-5$, $y=-11$ (whole number point), when $x=-10$, $y=\frac{3}{5}(-10)-8=-6 - 8=-14$ (whole number point).
# Answer:
Starting from the y - intercept $(0,-8)$:
- For $x = 5$, $y=-5$ (point $(5,-5)$)
- For $x = 10$, $y=-2$ (point $(10,-2)$)
- For $x=-5$, $y=-11$ (point $(-5,-11)$)
- For $x=-10$, $y=-14$ (point $(-10,-14)$)

These are some of the whole - number points that can be plotted using the rate of change.

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QUESTION IMAGE

Question

Explanation:

e)

Step1: Recall slope - intercept form

Step2: Identify \(b\) in the given function

Step1: Recall the definition of y - intercept

Step2: Determine the location on the graph

Step1: Recall the slope - intercept form

Step2: Identify \(m\) in the given function

Answer:

f)