QuestionWho has a steeper slope: Marty's function $v+3=\frac{1}{3}(x+9)$ or Ethan's from the table of values?

Studdy Solution

STEP 1

Assumptions1. Marty's function is given by $v+3=\frac{1}{3}(x+9)$ . Ethan's function is not given, but a table of $x$ and $y$ values is provided3. The slope of Marty's function is $1 /3$
4. The slope of a function is the change in $y$ divided by the change in $x$

STEP 2

First, we need to find the slope of Ethan's function. We can do this by using the formula for the slope of a function, which is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, let's pick two points from the table to calculate the slope of Ethan's function. We'll use the points $(-,9.2)$ and $(2,10.)$ .
$lope = \frac{10. -9.2}{2 - (-)}$

STEP 4

Calculate the slope of Ethan's function.
$lope = \frac{10.4 -9.2}{2 - (-4)} = \frac{1.2}{6} =0.2$

STEP 5

Now that we have the slopes of both functions, we can compare them to see which one is larger. Marty's slope is $1 /3$ and Ethan's slope is $0.2$ .

STEP 6

Compare the slopes.
$1 /3 >0.2$ Therefore, Marty's function has the larger slope.

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QuestionWho has a steeper slope: Marty's function $v+3=\frac{1}{3}(x+9)$ or Ethan's from the table of values?

Studdy Solution

STEP 1

Assumptions1. Marty's function is given by $v+3=\frac{1}{3}(x+9)$ . Ethan's function is not given, but a table of $x$ and $y$ values is provided3. The slope of Marty's function is $1 /3$
4. The slope of a function is the change in $y$ divided by the change in $x$

STEP 2

First, we need to find the slope of Ethan's function. We can do this by using the formula for the slope of a function, which is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, let's pick two points from the table to calculate the slope of Ethan's function. We'll use the points $(-,9.2)$ and $(2,10.)$ .
$lope = \frac{10. -9.2}{2 - (-)}$

STEP 4

Calculate the slope of Ethan's function.
$lope = \frac{10.4 -9.2}{2 - (-4)} = \frac{1.2}{6} =0.2$

STEP 5

Now that we have the slopes of both functions, we can compare them to see which one is larger. Marty's slope is $1 /3$ and Ethan's slope is $0.2$ .

STEP 6

Compare the slopes.
$1 /3 >0.2$ Therefore, Marty's function has the larger slope.

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QuestionWho has a steeper slope: Marty's function v+3=13(x+9)v+3=\frac{1}{3}(x+9)v+3=31​(x+9) or Ethan's from the table of values?

Studdy Solution

STEP 1

Assumptions1. Marty's function is given by v+3=13(x+9)v+3=\frac{1}{3}(x+9)v+3=31​(x+9). Ethan's function is not given, but a table of xxx and yyy values is provided3. The slope of Marty's function is 1/31 /31/34. The slope of a function is the change in yyy divided by the change in xxx

STEP 2

First, we need to find the slope of Ethan's function. We can do this by using the formula for the slope of a function, which is the change in yyy divided by the change in xxx.lope=ΔyΔxlope = \frac{\Delta y}{\Delta x}lope=ΔxΔy​

STEP 3

Now, let's pick two points from the table to calculate the slope of Ethan's function. We'll use the points (−,9.2)(-,9.2)(−,9.2) and (2,10.)(2,10.)(2,10.).lope=10.−9.22−(−)lope = \frac{10. -9.2}{2 - (-)}lope=2−(−)10.−9.2​

STEP 4

Calculate the slope of Ethan's function.lope=10.4−9.22−(−4)=1.26=0.2lope = \frac{10.4 -9.2}{2 - (-4)} = \frac{1.2}{6} =0.2lope=2−(−4)10.4−9.2​=61.2​=0.2

STEP 5

Now that we have the slopes of both functions, we can compare them to see which one is larger. Marty's slope is 1/31 /31/3 and Ethan's slope is 0.20.20.2.

STEP 6

Compare the slopes.1/3>0.21 /3 >0.21/3>0.2Therefore, Marty's function has the larger slope.

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QuestionWho has a steeper slope: Marty's function $v+3=\frac{1}{3}(x+9)$ or Ethan's from the table of values?

Assumptions1. Marty's function is given by $v+3=\frac{1}{3}(x+9)$ . Ethan's function is not given, but a table of $x$ and $y$ values is provided3. The slope of Marty's function is $1 /3$
4. The slope of a function is the change in $y$ divided by the change in $x$

First, we need to find the slope of Ethan's function. We can do this by using the formula for the slope of a function, which is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

Now, let's pick two points from the table to calculate the slope of Ethan's function. We'll use the points $(-,9.2)$ and $(2,10.)$ .
$lope = \frac{10. -9.2}{2 - (-)}$

Calculate the slope of Ethan's function.
$lope = \frac{10.4 -9.2}{2 - (-4)} = \frac{1.2}{6} =0.2$

Now that we have the slopes of both functions, we can compare them to see which one is larger. Marty's slope is $1 /3$ and Ethan's slope is $0.2$ .

Compare the slopes.
$1 /3 >0.2$ Therefore, Marty's function has the larger slope.