QuestionFind the slope and $y$ -intercept of the line from $3x - 2y = 6$ and graph it.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $3x -y =6$ . . The equation is in standard form, Ax + By = C, where A, B, and C are integers.
3. We need to find the slope and y-intercept of the line.
4. The slope of a line in slope-intercept form (y = mx + b) is represented by m.
5. The y-intercept of a line in slope-intercept form (y = mx + b) is represented by b.

STEP 2

First, we need to convert the equation from standard form to slope-intercept form. The slope-intercept form of a linear equation is $y = mx + b$ , where m is the slope and b is the y-intercept.To do this, we need to isolate y in the given equation. $x -2y =6$

STEP 3

Subtract $3x$ from both sides of the equation to isolate the term with y.
$-2y = -3x +6$

STEP 4

Next, divide every term by -2 to solve for y.
$y = \frac{-3x}{-2} + \frac{6}{-2}$

STEP 5

implify the equation.
$y = \frac{3}{2}x -3$

STEP 6

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
So, the slope of the line is $\frac{3}{2}$ and the y-intercept is $-3$ .

STEP 7

To graph the line, start by plotting the y-intercept (0, -3) on the y-axis.

STEP 8

From the y-intercept, use the slope to find the next point. The slope is $\frac{3}{2}$ , which means for every2 units you move to the right (positive direction on the x-axis), you move3 units up (positive direction on the y-axis).

STEP 9

Draw the line that passes through these points.
The slope of the line is $\frac{3}{2}$ and the y-intercept is -3.

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QuestionFind the slope and $y$ -intercept of the line from $3x - 2y = 6$ and graph it.

Studdy Solution

STEP 1

STEP 2

First, we need to convert the equation from standard form to slope-intercept form. The slope-intercept form of a linear equation is $y = mx + b$ , where m is the slope and b is the y-intercept.To do this, we need to isolate y in the given equation. $x -2y =6$

STEP 3

Subtract $3x$ from both sides of the equation to isolate the term with y.
$-2y = -3x +6$

STEP 4

Next, divide every term by -2 to solve for y.
$y = \frac{-3x}{-2} + \frac{6}{-2}$

STEP 5

implify the equation.
$y = \frac{3}{2}x -3$

STEP 6

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
So, the slope of the line is $\frac{3}{2}$ and the y-intercept is $-3$ .

STEP 7

To graph the line, start by plotting the y-intercept (0, -3) on the y-axis.

STEP 8

From the y-intercept, use the slope to find the next point. The slope is $\frac{3}{2}$ , which means for every2 units you move to the right (positive direction on the x-axis), you move3 units up (positive direction on the y-axis).

STEP 9

Draw the line that passes through these points.
The slope of the line is $\frac{3}{2}$ and the y-intercept is -3.

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QuestionFind the slope and yyy-intercept of the line from 3x−2y=63x - 2y = 63x−2y=6 and graph it.

Studdy Solution

STEP 1

STEP 2

First, we need to convert the equation from standard form to slope-intercept form. The slope-intercept form of a linear equation is y=mx+by = mx + by=mx+b, where m is the slope and b is the y-intercept.To do this, we need to isolate y in the given equation.x−2y=6x -2y =6x−2y=6

STEP 3

Subtract 3x3x3x from both sides of the equation to isolate the term with y.−2y=−3x+6-2y = -3x +6−2y=−3x+6

STEP 4

Next, divide every term by -2 to solve for y.y=−3x−2+6−2y = \frac{-3x}{-2} + \frac{6}{-2}y=−2−3x​+−26​

STEP 5

implify the equation.y=32x−3y = \frac{3}{2}x -3y=23​x−3

STEP 6

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.So, the slope of the line is 32\frac{3}{2}23​ and the y-intercept is −3-3−3.

STEP 7

To graph the line, start by plotting the y-intercept (0, -3) on the y-axis.

STEP 8

From the y-intercept, use the slope to find the next point. The slope is 32\frac{3}{2}23​, which means for every2 units you move to the right (positive direction on the x-axis), you move3 units up (positive direction on the y-axis).

STEP 9

Draw the line that passes through these points.The slope of the line is 32\frac{3}{2}23​ and the y-intercept is -3.

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QuestionFind the slope and $y$ -intercept of the line from $3x - 2y = 6$ and graph it.

First, we need to convert the equation from standard form to slope-intercept form. The slope-intercept form of a linear equation is $y = mx + b$ , where m is the slope and b is the y-intercept.To do this, we need to isolate y in the given equation. $x -2y =6$

Subtract $3x$ from both sides of the equation to isolate the term with y.
$-2y = -3x +6$

Next, divide every term by -2 to solve for y.
$y = \frac{-3x}{-2} + \frac{6}{-2}$

implify the equation.
$y = \frac{3}{2}x -3$

Now that we have the equation in slope-intercept form, we can identify the slope and the y-intercept.The slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
So, the slope of the line is $\frac{3}{2}$ and the y-intercept is $-3$ .

From the y-intercept, use the slope to find the next point. The slope is $\frac{3}{2}$ , which means for every2 units you move to the right (positive direction on the x-axis), you move3 units up (positive direction on the y-axis).

Draw the line that passes through these points.
The slope of the line is $\frac{3}{2}$ and the y-intercept is -3.