QuestionFind the slope, $y$ -intercept, and equation for the points (16, -1), (12, -2), (8, -3), (4, -4).

Studdy Solution

STEP 1

Assumptions1. The given values are points on a line in a two-dimensional space. . The line is linear and has a constant slope.
3. The equation of the line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is calculated as the change in $y$ divided by the change in $x$ .
$m = \frac{\Delta y}{\Delta x} = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $y2$ , $y1$ , $x2$ , and $x1$ to calculate the slope. We can use any two points from the table, but for simplicity, let's use the first two points (16, -1) and (12, -2).
$m = \frac{-2 - (-1)}{12 -16}$

STEP 4

Calculate the slope.
$m = \frac{-1}{-4} =0.25$

STEP 5

Now that we have the slope, we can find the y-intercept. The y-intercept is the value of $y$ when $x =0$ . We can find this by rearranging the equation of the line and solving for $c$ .
$c = y - mx$

STEP 6

Plug in the values for $m$ , $x$ , and $y$ from any point on the line. Let's use the first point (16, -1) for simplicity.
$c = -1 -0.25 \times16$

STEP 7

Calculate the y-intercept.
$c = -1 -4 = -5$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

STEP 9

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =.25x -5$ The equation of the line is $y =.25x -5$ .

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QuestionFind the slope, $y$ -intercept, and equation for the points (16, -1), (12, -2), (8, -3), (4, -4).

Studdy Solution

STEP 1

Assumptions1. The given values are points on a line in a two-dimensional space. . The line is linear and has a constant slope.
3. The equation of the line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is calculated as the change in $y$ divided by the change in $x$ .
$m = \frac{\Delta y}{\Delta x} = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $y2$ , $y1$ , $x2$ , and $x1$ to calculate the slope. We can use any two points from the table, but for simplicity, let's use the first two points (16, -1) and (12, -2).
$m = \frac{-2 - (-1)}{12 -16}$

STEP 4

Calculate the slope.
$m = \frac{-1}{-4} =0.25$

STEP 5

Now that we have the slope, we can find the y-intercept. The y-intercept is the value of $y$ when $x =0$ . We can find this by rearranging the equation of the line and solving for $c$ .
$c = y - mx$

STEP 6

Plug in the values for $m$ , $x$ , and $y$ from any point on the line. Let's use the first point (16, -1) for simplicity.
$c = -1 -0.25 \times16$

STEP 7

Calculate the y-intercept.
$c = -1 -4 = -5$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

STEP 9

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =.25x -5$ The equation of the line is $y =.25x -5$ .

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QuestionFind the slope, yyy-intercept, and equation for the points (16, -1), (12, -2), (8, -3), (4, -4).

Studdy Solution

STEP 1

Assumptions1. The given values are points on a line in a two-dimensional space. . The line is linear and has a constant slope.3. The equation of the line is in the form y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is calculated as the change in yyy divided by the change in xxx.m=ΔyΔx=y2−y1x2−x1m = \frac{\Delta y}{\Delta x} = \frac{y2 - y1}{x2 - x1}m=ΔxΔy​=x2−x1y2−y1​

STEP 3

Now, plug in the given values for y2y2y2, y1y1y1, x2x2x2, and x1x1x1 to calculate the slope. We can use any two points from the table, but for simplicity, let's use the first two points (16, -1) and (12, -2).m=−2−(−1)12−16m = \frac{-2 - (-1)}{12 -16}m=12−16−2−(−1)​

STEP 4

Calculate the slope.m=−1−4=0.25m = \frac{-1}{-4} =0.25m=−4−1​=0.25

STEP 5

Now that we have the slope, we can find the y-intercept. The y-intercept is the value of yyy when x=0x =0x=0. We can find this by rearranging the equation of the line and solving for ccc.c=y−mxc = y - mxc=y−mx

STEP 6

Plug in the values for mmm, xxx, and yyy from any point on the line. Let's use the first point (16, -1) for simplicity.c=−1−0.25×16c = -1 -0.25 \times16c=−1−0.25×16

STEP 7

Calculate the y-intercept.c=−1−4=−5c = -1 -4 = -5c=−1−4=−5

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.y=mx+cy = mx + cy=mx+c

STEP 9

Plug in the values for mmm and ccc to write the equation of the line.y=.25x−5y =.25x -5y=.25x−5The equation of the line is y=.25x−5y =.25x -5y=.25x−5.

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QuestionFind the slope, $y$ -intercept, and equation for the points (16, -1), (12, -2), (8, -3), (4, -4).

Assumptions1. The given values are points on a line in a two-dimensional space. . The line is linear and has a constant slope.
3. The equation of the line is in the form $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

First, we need to find the slope of the line. The slope is calculated as the change in $y$ divided by the change in $x$ .
$m = \frac{\Delta y}{\Delta x} = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for $y2$ , $y1$ , $x2$ , and $x1$ to calculate the slope. We can use any two points from the table, but for simplicity, let's use the first two points (16, -1) and (12, -2).
$m = \frac{-2 - (-1)}{12 -16}$

Calculate the slope.
$m = \frac{-1}{-4} =0.25$

Now that we have the slope, we can find the y-intercept. The y-intercept is the value of $y$ when $x =0$ . We can find this by rearranging the equation of the line and solving for $c$ .
$c = y - mx$

Plug in the values for $m$ , $x$ , and $y$ from any point on the line. Let's use the first point (16, -1) for simplicity.
$c = -1 -0.25 \times16$

Calculate the y-intercept.
$c = -1 -4 = -5$

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + c$

Plug in the values for $m$ and $c$ to write the equation of the line.
$y =.25x -5$ The equation of the line is $y =.25x -5$ .