Write a linear function $$ f $$ that has the indicated values. Sketch the graph of $$ f $$. $$ f(-5)=-15, f(2)=13 $$ $$ f(x)=\square $$ (Simplify your answer. Type an expression using $$ x $$ as the variable. Type your answer in slope-intercept form.) Use the graphing tool to graph the function. Click to enlarge graph

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UpStudy AI · Accepted Answer

To find the linear function $$ f(x) $$ that satisfies $$ f(-5) = -15 $$ and $$ f(2) = 13 $$, we'll follow these steps:

### 1. Find the Slope ($$ m $$)
The slope of a linear function can be calculated using two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points $$(-5, -15)$$ and $$(2, 13)$$:

$$
m = \frac{13 - (-15)}{2 - (-5)} = \frac{28}{7} = 4
$$

### 2. Find the Y-Intercept ($$ b $$)
Using the slope-intercept form $$ f(x) = mx + b $$ and one of the points (let's use $$(2, 13)$$):

$$
13 = 4(2) + b \
13 = 8 + b \
b = 13 - 8 \
b = 5
$$

### 3. Write the Function
Now that we have both $$ m $$ and $$ b $$:

$$
f(x) = 4x + 5
$$

### 4. Graph the Function
To sketch the graph of $$ f(x) = 4x + 5 $$:

1. **Y-Intercept:** Start at the point $$ (0, 5) $$ on the y-axis.
2. **Slope:** From the y-intercept, use the slope $$ m = 4 $$, which means "rise over run" is $$ 4/1 $$. Move up 4 units and right 1 unit to find another point.
3. **Plot the Points:** Using the given points $$(-5, -15)$$ and $$(2, 13)$$, plot these on the graph to ensure they lie on the line.
4. **Draw the Line:** Connect the points with a straight line, extending in both directions.

Here's a simple representation of the graph:

```
y
|
20|               *
15|            *
10|         *
5 |      *
0 |-------------------------- x
-5|  *
-10|
-15|
```

- The point $$ (0, 5) $$ is the y-intercept.
- The point $$ (2, 13) $$ is another point on the line.
- The point $$ (-5, -15) $$ is also on the line.

### Final Answer
$$
f(x) = 4x + 5
$$
$$ f(x) = 4x + 5 $$

Write a linear function that has the indicated values. Sketch
the graph of .

(Simplify your answer. Type an expression using as the
variable. Type your answer in slope-intercept form.)
Use the graphing tool to graph the function.
Click to
enlarge
graph

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Write a linear function that has the indicated values. Sketch the graph of . (Simplify your answer. Type an expression using as the variable. Type your answer in slope-intercept form.) Use the graphing tool to graph the function. Click to enlarge graph