QuestionFind the slope, $y$ -intercept, and equation of the line for the values: (1, 9), (2, 16), (3, 23), (4, 30).

Studdy Solution

STEP 1

Assumptions1. The given table of values for $x$ and $y$ represents a linear relationship. . The slope of the line can be calculated using any two points from the table.
3. The $y$ -intercept is the value of $y$ when $x=0$ .
4. 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 the change in $y$ divided by the change in $x$ , which can be calculated using any two points from the table.
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Let's use the first two points from the table to calculate the slope. $m = \frac{16 -9}{2 -1}$

STEP 4

Calculate the slope.
$m = \frac{16 -9}{2 -1} =7$

STEP 5

Now that we have the slope, we need to find the $y$ -intercept. To do this, we can use the equation of the line $y=mx+c$ and solve for $c$ .
$c = y - mx$

STEP 6

Let's use the first point from the table to calculate the $y$ -intercept.
$c =9 - \times1$

STEP 7

Calculate the $y$ -intercept.
$c =9 -7 \times1 =2$

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 the slope and the $y$ -intercept to write the equation of the line.
$y =7x +2$ The slope of the line is7, the $y$ -intercept is2, and the equation of the line is $y =7x +2$ .

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QuestionFind the slope, $y$ -intercept, and equation of the line for the values: (1, 9), (2, 16), (3, 23), (4, 30).

Studdy Solution

STEP 1

STEP 2

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ , which can be calculated using any two points from the table.
$m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Let's use the first two points from the table to calculate the slope. $m = \frac{16 -9}{2 -1}$

STEP 4

Calculate the slope.
$m = \frac{16 -9}{2 -1} =7$

STEP 5

Now that we have the slope, we need to find the $y$ -intercept. To do this, we can use the equation of the line $y=mx+c$ and solve for $c$ .
$c = y - mx$

STEP 6

Let's use the first point from the table to calculate the $y$ -intercept.
$c =9 - \times1$

STEP 7

Calculate the $y$ -intercept.
$c =9 -7 \times1 =2$

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 the slope and the $y$ -intercept to write the equation of the line.
$y =7x +2$ The slope of the line is7, the $y$ -intercept is2, and the equation of the line is $y =7x +2$ .

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QuestionFind the slope, yyy-intercept, and equation of the line for the values: (1, 9), (2, 16), (3, 23), (4, 30).

Studdy Solution

STEP 1

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, which can be calculated using any two points from the table.m=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Let's use the first two points from the table to calculate the slope.m=16−92−1m = \frac{16 -9}{2 -1}m=2−116−9​

STEP 4

Calculate the slope.m=16−92−1=7m = \frac{16 -9}{2 -1} =7m=2−116−9​=7

STEP 5

Now that we have the slope, we need to find the yyy-intercept. To do this, we can use the equation of the line y=mx+cy=mx+cy=mx+c and solve for ccc.c=y−mxc = y - mxc=y−mx

STEP 6

Let's use the first point from the table to calculate the yyy-intercept.c=9−×1c =9 - \times1c=9−×1

STEP 7

Calculate the yyy-intercept.c=9−7×1=2c =9 -7 \times1 =2c=9−7×1=2

STEP 8

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

STEP 9

Plug in the values for the slope and the yyy-intercept to write the equation of the line.y=7x+2y =7x +2y=7x+2The slope of the line is7, the yyy-intercept is2, and the equation of the line is y=7x+2y =7x +2y=7x+2.

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QuestionFind the slope, $y$ -intercept, and equation of the line for the values: (1, 9), (2, 16), (3, 23), (4, 30).

First, we need to find the slope of the line. The slope is the change in $y$ divided by the change in $x$ , which can be calculated using any two points from the table.
$m = \frac{y2 - y1}{x2 - x1}$

Let's use the first two points from the table to calculate the slope. $m = \frac{16 -9}{2 -1}$

Calculate the slope.
$m = \frac{16 -9}{2 -1} =7$

Now that we have the slope, we need to find the $y$ -intercept. To do this, we can use the equation of the line $y=mx+c$ and solve for $c$ .
$c = y - mx$

Let's use the first point from the table to calculate the $y$ -intercept.
$c =9 - \times1$

Calculate the $y$ -intercept.
$c =9 -7 \times1 =2$

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 the slope and the $y$ -intercept to write the equation of the line.
$y =7x +2$ The slope of the line is7, the $y$ -intercept is2, and the equation of the line is $y =7x +2$ .