QuestionFind the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Studdy Solution

STEP 1

Assumptions1. The function is linear, as suggested by the constant rate of change in the table. . The $y$ -intercept is the value of $y$ when $x =0$ .

STEP 2

We first need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, plug in the given values for $\Delta y$ and $\Delta x$ to calculate the slope. We can use any two points from the table for this. Let's use the points (1,8) and (2,6).
$lope = \frac{6 -8}{2 -1}$

STEP 4

Calculate the slope.
$lope = \frac{-2}{1} = -2$

STEP 5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is $y - y1 = m(x - x1)$ , where $m$ is the slope and $(x1, y1)$ is a point on the line.

STEP 6

Plug in the values for the slope and a point on the line to find the equation of the line. Let's use the point (1,8).
$y -8 = -2(x -1)$

STEP 7

implify the equation.
$y - = -2x +2$

STEP 8

Rearrange the equation to solve for $y$ .
$y = -2x +10$

STEP 9

Now that we have the equation of the line, we can find the $y$ -intercept by setting $x =$ .
$y = -2() +$

STEP 10

Calculate the $y$ -intercept.
$y =0 +10 =10$ The $y$ -intercept of the function is10.

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QuestionFind the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Studdy Solution

STEP 1

Assumptions1. The function is linear, as suggested by the constant rate of change in the table. . The $y$ -intercept is the value of $y$ when $x =0$ .

STEP 2

We first need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, plug in the given values for $\Delta y$ and $\Delta x$ to calculate the slope. We can use any two points from the table for this. Let's use the points (1,8) and (2,6).
$lope = \frac{6 -8}{2 -1}$

STEP 4

Calculate the slope.
$lope = \frac{-2}{1} = -2$

STEP 5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is $y - y1 = m(x - x1)$ , where $m$ is the slope and $(x1, y1)$ is a point on the line.

STEP 6

Plug in the values for the slope and a point on the line to find the equation of the line. Let's use the point (1,8).
$y -8 = -2(x -1)$

STEP 7

implify the equation.
$y - = -2x +2$

STEP 8

Rearrange the equation to solve for $y$ .
$y = -2x +10$

STEP 9

Now that we have the equation of the line, we can find the $y$ -intercept by setting $x =$ .
$y = -2() +$

STEP 10

Calculate the $y$ -intercept.
$y =0 +10 =10$ The $y$ -intercept of the function is10.

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QuestionFind the yyy-intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Studdy Solution

STEP 1

Assumptions1. The function is linear, as suggested by the constant rate of change in the table. . The yyy-intercept is the value of yyy when x=0x =0x=0.

STEP 2

We first need to find the slope of the function. The slope is the change in yyy divided by the change in xxx.lope=ΔyΔxlope = \frac{\Delta y}{\Delta x}lope=ΔxΔy​

STEP 3

Now, plug in the given values for Δy\Delta yΔy and Δx\Delta xΔx to calculate the slope. We can use any two points from the table for this. Let's use the points (1,8) and (2,6).lope=6−82−1lope = \frac{6 -8}{2 -1}lope=2−16−8​

STEP 4

Calculate the slope.lope=−21=−2lope = \frac{-2}{1} = -2lope=1−2​=−2

STEP 5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is y−y1=m(x−x1)y - y1 = m(x - x1)y−y1=m(x−x1), where mmm is the slope and (x1,y1)(x1, y1)(x1,y1) is a point on the line.

STEP 6

Plug in the values for the slope and a point on the line to find the equation of the line. Let's use the point (1,8).y−8=−2(x−1)y -8 = -2(x -1)y−8=−2(x−1)

STEP 7

implify the equation.y−=−2x+2y - = -2x +2y−=−2x+2

STEP 8

Rearrange the equation to solve for yyy.y=−2x+10y = -2x +10y=−2x+10

STEP 9

Now that we have the equation of the line, we can find the yyy-intercept by setting x=x =x=.y=−2()+y = -2() +y=−2()+

STEP 10

Calculate the yyy-intercept.y=0+10=10y =0 +10 =10y=0+10=10The yyy-intercept of the function is10.

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QuestionFind the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Assumptions1. The function is linear, as suggested by the constant rate of change in the table. . The $y$ -intercept is the value of $y$ when $x =0$ .

We first need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ .
$lope = \frac{\Delta y}{\Delta x}$

Now, plug in the given values for $\Delta y$ and $\Delta x$ to calculate the slope. We can use any two points from the table for this. Let's use the points (1,8) and (2,6).
$lope = \frac{6 -8}{2 -1}$

Calculate the slope.
$lope = \frac{-2}{1} = -2$

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is $y - y1 = m(x - x1)$ , where $m$ is the slope and $(x1, y1)$ is a point on the line.

Plug in the values for the slope and a point on the line to find the equation of the line. Let's use the point (1,8).
$y -8 = -2(x -1)$

implify the equation.
$y - = -2x +2$

Rearrange the equation to solve for $y$ .
$y = -2x +10$

Now that we have the equation of the line, we can find the $y$ -intercept by setting $x =$ .
$y = -2() +$

Calculate the $y$ -intercept.
$y =0 +10 =10$ The $y$ -intercept of the function is10.