QuestionFind the slope and $y$ -intercept of the line given by $-6x - 2y = 4$ . Then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $-6x -y =4$ . We are to find the slope and the y-intercept of the line3. The standard form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept

STEP 2

First, we need to rewrite the given equation in the standard form. We can do this by isolating $y$ on one side of the equation.
$-2y =6x +4$

STEP 3

Now, divide every term in the equation by $-2$ to solve for $y$ .
$y = -3x -2$

STEP 4

From the standard form of the equation, we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.
$m = -3, c = -2$ So, the slope of the line is $-3$ and the y-intercept is $-2$ .

STEP 5

To graph the line, start by plotting the y-intercept on the y-axis. This is the point $(0, -2)$ .

STEP 6

Then, use the slope to find another point on the line. The slope is the ratio of the change in $y$ to the change in $x$ . Since the slope is $-3$ , this means that for every1 unit increase in $x$ , $y$ decreases by3 units.

STEP 7

From the y-intercept $(0, -2)$ , move1 unit to the right and3 units down to get to the point $(1, -5)$ . Plot this point on the graph.

STEP 8

Finally, draw a straight line through the two points. This line represents the equation $-6x -2y =4$ .
The slope of the line is $-3$ and the y-intercept is $-2$ .

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QuestionFind the slope and $y$ -intercept of the line given by $-6x - 2y = 4$ . Then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $-6x -y =4$ . We are to find the slope and the y-intercept of the line3. The standard form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept

STEP 2

First, we need to rewrite the given equation in the standard form. We can do this by isolating $y$ on one side of the equation.
$-2y =6x +4$

STEP 3

Now, divide every term in the equation by $-2$ to solve for $y$ .
$y = -3x -2$

STEP 4

From the standard form of the equation, we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.
$m = -3, c = -2$ So, the slope of the line is $-3$ and the y-intercept is $-2$ .

STEP 5

To graph the line, start by plotting the y-intercept on the y-axis. This is the point $(0, -2)$ .

STEP 6

Then, use the slope to find another point on the line. The slope is the ratio of the change in $y$ to the change in $x$ . Since the slope is $-3$ , this means that for every1 unit increase in $x$ , $y$ decreases by3 units.

STEP 7

From the y-intercept $(0, -2)$ , move1 unit to the right and3 units down to get to the point $(1, -5)$ . Plot this point on the graph.

STEP 8

Finally, draw a straight line through the two points. This line represents the equation $-6x -2y =4$ .
The slope of the line is $-3$ and the y-intercept is $-2$ .

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QuestionFind the slope and yyy-intercept of the line given by −6x−2y=4-6x - 2y = 4−6x−2y=4. Then graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as −6x−y=4-6x -y =4−6x−y=4 . We are to find the slope and the y-intercept of the line3. The standard form of a linear equation is y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept

STEP 2

First, we need to rewrite the given equation in the standard form. We can do this by isolating yyy on one side of the equation.−2y=6x+4-2y =6x +4−2y=6x+4

STEP 3

Now, divide every term in the equation by −2-2−2 to solve for yyy.y=−3x−2y = -3x -2y=−3x−2

STEP 4

From the standard form of the equation, we can identify the slope and the y-intercept. The slope mmm is the coefficient of xxx and the y-intercept ccc is the constant term.m=−3,c=−2m = -3, c = -2m=−3,c=−2So, the slope of the line is −3-3−3 and the y-intercept is −2-2−2.

STEP 5

To graph the line, start by plotting the y-intercept on the y-axis. This is the point (0,−2)(0, -2)(0,−2).

STEP 6

Then, use the slope to find another point on the line. The slope is the ratio of the change in yyy to the change in xxx. Since the slope is −3-3−3, this means that for every1 unit increase in xxx, yyy decreases by3 units.

STEP 7

From the y-intercept (0,−2)(0, -2)(0,−2), move1 unit to the right and3 units down to get to the point (1,−5)(1, -5)(1,−5). Plot this point on the graph.

STEP 8

Finally, draw a straight line through the two points. This line represents the equation −6x−2y=4-6x -2y =4−6x−2y=4.The slope of the line is −3-3−3 and the y-intercept is −2-2−2.

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QuestionFind the slope and $y$ -intercept of the line given by $-6x - 2y = 4$ . Then graph the line.

Assumptions1. The equation of the line is given as $-6x -y =4$ . We are to find the slope and the y-intercept of the line3. The standard form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept

First, we need to rewrite the given equation in the standard form. We can do this by isolating $y$ on one side of the equation.
$-2y =6x +4$

Now, divide every term in the equation by $-2$ to solve for $y$ .
$y = -3x -2$

From the standard form of the equation, we can identify the slope and the y-intercept. The slope $m$ is the coefficient of $x$ and the y-intercept $c$ is the constant term.
$m = -3, c = -2$ So, the slope of the line is $-3$ and the y-intercept is $-2$ .

To graph the line, start by plotting the y-intercept on the y-axis. This is the point $(0, -2)$ .

Then, use the slope to find another point on the line. The slope is the ratio of the change in $y$ to the change in $x$ . Since the slope is $-3$ , this means that for every1 unit increase in $x$ , $y$ decreases by3 units.

From the y-intercept $(0, -2)$ , move1 unit to the right and3 units down to get to the point $(1, -5)$ . Plot this point on the graph.

Finally, draw a straight line through the two points. This line represents the equation $-6x -2y =4$ .
The slope of the line is $-3$ and the y-intercept is $-2$ .