QuestionFind the slope, $y$ -intercept, and equation of the line through points (-6, 17), (-2, 11), (2, 5), (6, -1).

Studdy Solution

STEP 1

Assumptions1. The given table represents a linear relationship between $x$ and $y$ . . We need to find the slope, $y$ -intercept, and equation of the line represented by the table.

STEP 2

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ . $lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, we can calculate the slope using the given values from the table. For example, we can use the points (-6,17) and (-2,11).
$lope = \frac{y2 - y1}{x2 - x1} = \frac{11 -17}{-2 - (-6)}$

STEP 4

Calculate the slope.
$lope = \frac{11 -17}{-2 - (-6)} = \frac{-6}{4} = -1.$

STEP 5

Now that we have the slope, we can find the $y$ -intercept. The $y$ -intercept is the $y$ value when $x =0$ . We can find this by using the slope and one of the points from the table in the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
$y = mx + b$

STEP 6

Substitute the slope and one of the points into the equation to solve for $b$ . Let's use the point (-2,11).
$11 = -1.5 \cdot -2 + b$

STEP 7

olve for $b$ .
$11 =3 + b$ $b =11 -3 =$

STEP 8

Now that we have the slope and the $y$ -intercept, we can write the equation of the line. The equation of a line is $y = mx + b$ .
$y = -1.5x +8$ The slope of the line is -1.5, the $y$ -intercept is8, and the equation of the line is $y = -1.5x +8$ .

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QuestionFind the slope, $y$ -intercept, and equation of the line through points (-6, 17), (-2, 11), (2, 5), (6, -1).

Studdy Solution

STEP 1

Assumptions1. The given table represents a linear relationship between $x$ and $y$ . . We need to find the slope, $y$ -intercept, and equation of the line represented by the table.

STEP 2

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ . $lope = \frac{\Delta y}{\Delta x}$

STEP 3

Now, we can calculate the slope using the given values from the table. For example, we can use the points (-6,17) and (-2,11).
$lope = \frac{y2 - y1}{x2 - x1} = \frac{11 -17}{-2 - (-6)}$

STEP 4

Calculate the slope.
$lope = \frac{11 -17}{-2 - (-6)} = \frac{-6}{4} = -1.$

STEP 5

Now that we have the slope, we can find the $y$ -intercept. The $y$ -intercept is the $y$ value when $x =0$ . We can find this by using the slope and one of the points from the table in the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
$y = mx + b$

STEP 6

Substitute the slope and one of the points into the equation to solve for $b$ . Let's use the point (-2,11).
$11 = -1.5 \cdot -2 + b$

STEP 7

olve for $b$ .
$11 =3 + b$ $b =11 -3 =$

STEP 8

Now that we have the slope and the $y$ -intercept, we can write the equation of the line. The equation of a line is $y = mx + b$ .
$y = -1.5x +8$ The slope of the line is -1.5, the $y$ -intercept is8, and the equation of the line is $y = -1.5x +8$ .

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QuestionFind the slope, yyy-intercept, and equation of the line through points (-6, 17), (-2, 11), (2, 5), (6, -1).

Studdy Solution

STEP 1

Assumptions1. The given table represents a linear relationship between xxx and yyy. . We need to find the slope, yyy-intercept, and equation of the line represented by the table.

STEP 2

First, we need to find the slope of the line. 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, we can calculate the slope using the given values from the table. For example, we can use the points (-6,17) and (-2,11).lope=y2−y1x2−x1=11−17−2−(−6)lope = \frac{y2 - y1}{x2 - x1} = \frac{11 -17}{-2 - (-6)}lope=x2−x1y2−y1​=−2−(−6)11−17​

STEP 4

Calculate the slope.lope=11−17−2−(−6)=−64=−1.lope = \frac{11 -17}{-2 - (-6)} = \frac{-6}{4} = -1.lope=−2−(−6)11−17​=4−6​=−1.

STEP 5

Now that we have the slope, we can find the yyy-intercept. The yyy-intercept is the yyy value when x=0x =0x=0. We can find this by using the slope and one of the points from the table in the equation y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the yyy-intercept.y=mx+by = mx + by=mx+b

STEP 6

Substitute the slope and one of the points into the equation to solve for bbb. Let's use the point (-2,11).11=−1.5⋅−2+b11 = -1.5 \cdot -2 + b11=−1.5⋅−2+b

STEP 7

olve for bbb.11=3+b11 =3 + b11=3+bb=11−3=b =11 -3 =b=11−3=

STEP 8

Now that we have the slope and the yyy-intercept, we can write the equation of the line. The equation of a line is y=mx+by = mx + by=mx+b.y=−1.5x+8y = -1.5x +8y=−1.5x+8The slope of the line is -1.5, the yyy-intercept is8, and the equation of the line is y=−1.5x+8y = -1.5x +8y=−1.5x+8.

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QuestionFind the slope, $y$ -intercept, and equation of the line through points (-6, 17), (-2, 11), (2, 5), (6, -1).

Assumptions1. The given table represents a linear relationship between $x$ and $y$ . . We need to find the slope, $y$ -intercept, and equation of the line represented by the table.

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ . $lope = \frac{\Delta y}{\Delta x}$

Now, we can calculate the slope using the given values from the table. For example, we can use the points (-6,17) and (-2,11).
$lope = \frac{y2 - y1}{x2 - x1} = \frac{11 -17}{-2 - (-6)}$

Calculate the slope.
$lope = \frac{11 -17}{-2 - (-6)} = \frac{-6}{4} = -1.$

Now that we have the slope, we can find the $y$ -intercept. The $y$ -intercept is the $y$ value when $x =0$ . We can find this by using the slope and one of the points from the table in the equation $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.
$y = mx + b$

Substitute the slope and one of the points into the equation to solve for $b$ . Let's use the point (-2,11).
$11 = -1.5 \cdot -2 + b$

olve for $b$ .
$11 =3 + b$ $b =11 -3 =$

Now that we have the slope and the $y$ -intercept, we can write the equation of the line. The equation of a line is $y = mx + b$ .
$y = -1.5x +8$ The slope of the line is -1.5, the $y$ -intercept is8, and the equation of the line is $y = -1.5x +8$ .