Question Find the linear function with $f(0)=6$ and slope $f=-9$ .

Studdy Solution

STEP 1

Assumptions
1. The function $f(x)$ is linear.
2. The value of the function at $x=0$ is $f(0)=6$ .
3. The slope of the function $f$ is $-9$ .

STEP 2

The general form of a linear function is given by:
$f(x) = mx + b$
where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Since we know the slope of the function $f$ is $-9$ , we can substitute $m$ with $-9$ in the general form.
$f(x) = -9x + b$

STEP 4

To find the y-intercept $b$ , we use the given point where $f(0)=6$ . Since $x=0$ at this point, we can substitute $x$ with $0$ in the function.
$f(0) = -9(0) + b$

STEP 5

Solve for $b$ using the known value of $f(0)$ .
$6 = 0 + b$

STEP 6

Since $0$ added to $b$ is simply $b$ , we have:
$b = 6$

STEP 7

Now that we have both the slope $m$ and the y-intercept $b$ , we can write the linear function $f(x)$ .
$f(x) = -9x + 6$
This is the linear function with the given properties.

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Question Find the linear function with $f(0)=6$ and slope $f=-9$ .

Studdy Solution

STEP 1

Assumptions
1. The function $f(x)$ is linear.
2. The value of the function at $x=0$ is $f(0)=6$ .
3. The slope of the function $f$ is $-9$ .

STEP 2

The general form of a linear function is given by:
$f(x) = mx + b$
where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Since we know the slope of the function $f$ is $-9$ , we can substitute $m$ with $-9$ in the general form.
$f(x) = -9x + b$

STEP 4

To find the y-intercept $b$ , we use the given point where $f(0)=6$ . Since $x=0$ at this point, we can substitute $x$ with $0$ in the function.
$f(0) = -9(0) + b$

STEP 5

Solve for $b$ using the known value of $f(0)$ .
$6 = 0 + b$

STEP 6

Since $0$ added to $b$ is simply $b$ , we have:
$b = 6$

STEP 7

Now that we have both the slope $m$ and the y-intercept $b$ , we can write the linear function $f(x)$ .
$f(x) = -9x + 6$
This is the linear function with the given properties.

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Question Find the linear function with f(0)=6f(0)=6f(0)=6 and slope f=−9f=-9f=−9.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is linear.2. The value of the function at x=0x=0x=0 is f(0)=6f(0)=6f(0)=6.3. The slope of the function fff is −9-9−9.

STEP 2

The general form of a linear function is given by:f(x)=mx+bf(x) = mx + bf(x)=mx+bwhere mmm is the slope and bbb is the y-intercept.

STEP 3

Since we know the slope of the function fff is −9-9−9, we can substitute mmm with −9-9−9 in the general form.f(x)=−9x+bf(x) = -9x + bf(x)=−9x+b

STEP 4

To find the y-intercept bbb, we use the given point where f(0)=6f(0)=6f(0)=6. Since x=0x=0x=0 at this point, we can substitute xxx with 000 in the function.f(0)=−9(0)+bf(0) = -9(0) + bf(0)=−9(0)+b

STEP 5

Solve for bbb using the known value of f(0)f(0)f(0).6=0+b6 = 0 + b6=0+b

STEP 6

Since 000 added to bbb is simply bbb, we have:b=6b = 6b=6

STEP 7

Now that we have both the slope mmm and the y-intercept bbb, we can write the linear function f(x)f(x)f(x).f(x)=−9x+6f(x) = -9x + 6f(x)=−9x+6This is the linear function with the given properties.

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Question Find the linear function with $f(0)=6$ and slope $f=-9$ .

Assumptions
1. The function $f(x)$ is linear.
2. The value of the function at $x=0$ is $f(0)=6$ .
3. The slope of the function $f$ is $-9$ .

The general form of a linear function is given by:
$f(x) = mx + b$
where $m$ is the slope and $b$ is the y-intercept.

Since we know the slope of the function $f$ is $-9$ , we can substitute $m$ with $-9$ in the general form.
$f(x) = -9x + b$

To find the y-intercept $b$ , we use the given point where $f(0)=6$ . Since $x=0$ at this point, we can substitute $x$ with $0$ in the function.
$f(0) = -9(0) + b$

Solve for $b$ using the known value of $f(0)$ .
$6 = 0 + b$

Since $0$ added to $b$ is simply $b$ , we have:
$b = 6$

Now that we have both the slope $m$ and the y-intercept $b$ , we can write the linear function $f(x)$ .
$f(x) = -9x + 6$
This is the linear function with the given properties.