QuestionFind the line parallel to $y=3x+6$ that passes through the point $(3,2)$ . What is its equation?

Studdy Solution

STEP 1

Assumptions1. The equation of the line we want to find is parallel to the line defined by the equation $y=3x+6$ . . The line we want to find goes through the point $(3,)$ .
3. The slope of a line given by the equation $y=mx+b$ is $m$ .
4. Two lines are parallel if and only if their slopes are equal.

STEP 2

First, we need to find the slope of the given line. We can do this by identifying the coefficient of $x$ in the equation of the line.
The equation of the given line is $y=x+6$ , so the slope of the line is $$.

STEP 3

Since the line we want to find is parallel to the given line, its slope is also $3$ .

STEP 4

The general form of the equation of a line is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know that the slope of the line we want to find is $3$ , so the equation of the line is $y=3x+b$ .

STEP 5

To find the y-intercept $b$ , we can use the fact that the line goes through the point $(3,2)$ . This means that when $x=3$ , $y=2$ . We can substitute these values into the equation of the line to solve for $b$ .
$2=3(3)+b$

STEP 6

olve the equation for $b$ .
$2=9+b$

STEP 7

Subtract $9$ from both sides of the equation to isolate $b$ .
$b=2-9$

STEP 8

Calculate the value of $b$ .
$b=-7$

STEP 9

Now that we have the y-intercept, we can write the equation of the line. Substitute $3$ for $m$ and $-7$ for $b$ in the equation $y=mx+b$ .
$y=3x-7$ The equation of the line that is parallel to the line defined by the equation $y=3x+6$ and goes through the point $(3,2)$ is $y=3x-7$ .

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QuestionFind the line parallel to $y=3x+6$ that passes through the point $(3,2)$ . What is its equation?

Studdy Solution

STEP 1

Assumptions1. The equation of the line we want to find is parallel to the line defined by the equation $y=3x+6$ . . The line we want to find goes through the point $(3,)$ .
3. The slope of a line given by the equation $y=mx+b$ is $m$ .
4. Two lines are parallel if and only if their slopes are equal.

STEP 2

First, we need to find the slope of the given line. We can do this by identifying the coefficient of $x$ in the equation of the line.
The equation of the given line is $y=x+6$ , so the slope of the line is $$.

STEP 3

Since the line we want to find is parallel to the given line, its slope is also $3$ .

STEP 4

The general form of the equation of a line is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know that the slope of the line we want to find is $3$ , so the equation of the line is $y=3x+b$ .

STEP 5

To find the y-intercept $b$ , we can use the fact that the line goes through the point $(3,2)$ . This means that when $x=3$ , $y=2$ . We can substitute these values into the equation of the line to solve for $b$ .
$2=3(3)+b$

STEP 6

olve the equation for $b$ .
$2=9+b$

STEP 7

Subtract $9$ from both sides of the equation to isolate $b$ .
$b=2-9$

STEP 8

Calculate the value of $b$ .
$b=-7$

STEP 9

Now that we have the y-intercept, we can write the equation of the line. Substitute $3$ for $m$ and $-7$ for $b$ in the equation $y=mx+b$ .
$y=3x-7$ The equation of the line that is parallel to the line defined by the equation $y=3x+6$ and goes through the point $(3,2)$ is $y=3x-7$ .

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QuestionFind the line parallel to y=3x+6y=3x+6y=3x+6 that passes through the point (3,2)(3,2)(3,2). What is its equation?

Studdy Solution

STEP 1

STEP 2

First, we need to find the slope of the given line. We can do this by identifying the coefficient of xxx in the equation of the line.The equation of the given line is y=x+6y=x+6y=x+6, so the slope of the line is $$.

STEP 3

Since the line we want to find is parallel to the given line, its slope is also 333.

STEP 4

The general form of the equation of a line is y=mx+by=mx+by=mx+b, where mmm is the slope and bbb is the y-intercept. We know that the slope of the line we want to find is 333, so the equation of the line is y=3x+by=3x+by=3x+b.

STEP 5

To find the y-intercept bbb, we can use the fact that the line goes through the point (3,2)(3,2)(3,2). This means that when x=3x=3x=3, y=2y=2y=2. We can substitute these values into the equation of the line to solve for bbb.2=3(3)+b2=3(3)+b2=3(3)+b

STEP 6

olve the equation for bbb.2=9+b2=9+b2=9+b

STEP 7

Subtract 999 from both sides of the equation to isolate bbb.b=2−9b=2-9b=2−9

STEP 8

Calculate the value of bbb.b=−7b=-7b=−7

STEP 9

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QuestionFind the line parallel to $y=3x+6$ that passes through the point $(3,2)$ . What is its equation?

First, we need to find the slope of the given line. We can do this by identifying the coefficient of $x$ in the equation of the line.
The equation of the given line is $y=x+6$ , so the slope of the line is $$.

Since the line we want to find is parallel to the given line, its slope is also $3$ .

The general form of the equation of a line is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know that the slope of the line we want to find is $3$ , so the equation of the line is $y=3x+b$ .

To find the y-intercept $b$ , we can use the fact that the line goes through the point $(3,2)$ . This means that when $x=3$ , $y=2$ . We can substitute these values into the equation of the line to solve for $b$ .
$2=3(3)+b$

olve the equation for $b$ .
$2=9+b$

Subtract $9$ from both sides of the equation to isolate $b$ .
$b=2-9$

Calculate the value of $b$ .
$b=-7$