QuestionFind the equation in point-slope form for a line through $(2,5)$ with slope 3: $y - [5] = [3](x - [2])$ .

Studdy Solution

STEP 1

Assumptions1. The line intersects the point $(,5)$ . The slope of the line is33. We need to substitute these values into the point-slope form of a line equation $y-y_{1}=m\left(x-x_{1}\right)$

STEP 2

The point-slope form of a line equation is $y-y_{1}=m\left(x-x_{1}\right)$ where $(x_{1},y_{1})$ is a point on the line and $m$ is the slope of the line.

STEP 3

Substitute the given point $(2,5)$ into the equation. This means $x_{1}=2$ and $y_{1}=5$ .
$y-5=m\left(x-2\right)$

STEP 4

Substitute the given slope $m=3$ into the equation.
$y-=3\left(x-2\right)$

STEP 5

This is the equation of the line in point-slope form. $y-5=3\left(x-2\right)$ The line that intersects the point $(2,5)$ and has a slope of3 is represented by the equation $y-5=3\left(x-2\right)$ .

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QuestionFind the equation in point-slope form for a line through $(2,5)$ with slope 3: $y - [5] = [3](x - [2])$ .

Studdy Solution

STEP 1

Assumptions1. The line intersects the point $(,5)$ . The slope of the line is33. We need to substitute these values into the point-slope form of a line equation $y-y_{1}=m\left(x-x_{1}\right)$

STEP 2

The point-slope form of a line equation is $y-y_{1}=m\left(x-x_{1}\right)$ where $(x_{1},y_{1})$ is a point on the line and $m$ is the slope of the line.

STEP 3

Substitute the given point $(2,5)$ into the equation. This means $x_{1}=2$ and $y_{1}=5$ .
$y-5=m\left(x-2\right)$

STEP 4

Substitute the given slope $m=3$ into the equation.
$y-=3\left(x-2\right)$

STEP 5

This is the equation of the line in point-slope form. $y-5=3\left(x-2\right)$ The line that intersects the point $(2,5)$ and has a slope of3 is represented by the equation $y-5=3\left(x-2\right)$ .

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QuestionFind the equation in point-slope form for a line through (2,5)(2,5)(2,5) with slope 3: y−[5]=[3](x−[2])y - [5] = [3](x - [2])y−[5]=[3](x−[2]).

Studdy Solution

STEP 1

Assumptions1. The line intersects the point (,5)(,5)(,5). The slope of the line is33. We need to substitute these values into the point-slope form of a line equation y−y1=m(x−x1)y-y_{1}=m\left(x-x_{1}\right)y−y1​=m(x−x1​)

STEP 2

The point-slope form of a line equation is y−y1=m(x−x1)y-y_{1}=m\left(x-x_{1}\right)y−y1​=m(x−x1​) where (x1,y1)(x_{1},y_{1})(x1​,y1​) is a point on the line and mmm is the slope of the line.

STEP 3

Substitute the given point (2,5)(2,5)(2,5) into the equation. This means x1=2x_{1}=2x1​=2 and y1=5y_{1}=5y1​=5.y−5=m(x−2)y-5=m\left(x-2\right)y−5=m(x−2)

STEP 4

Substitute the given slope m=3m=3m=3 into the equation.y−=3(x−2)y-=3\left(x-2\right)y−=3(x−2)

STEP 5

This is the equation of the line in point-slope form.y−5=3(x−2)y-5=3\left(x-2\right)y−5=3(x−2)The line that intersects the point (2,5)(2,5)(2,5) and has a slope of3 is represented by the equation y−5=3(x−2)y-5=3\left(x-2\right)y−5=3(x−2).

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QuestionFind the equation in point-slope form for a line through $(2,5)$ with slope 3: $y - [5] = [3](x - [2])$ .

Assumptions1. The line intersects the point $(,5)$ . The slope of the line is33. We need to substitute these values into the point-slope form of a line equation $y-y_{1}=m\left(x-x_{1}\right)$

The point-slope form of a line equation is $y-y_{1}=m\left(x-x_{1}\right)$ where $(x_{1},y_{1})$ is a point on the line and $m$ is the slope of the line.

Substitute the given point $(2,5)$ into the equation. This means $x_{1}=2$ and $y_{1}=5$ .
$y-5=m\left(x-2\right)$

Substitute the given slope $m=3$ into the equation.
$y-=3\left(x-2\right)$

This is the equation of the line in point-slope form. $y-5=3\left(x-2\right)$ The line that intersects the point $(2,5)$ and has a slope of3 is represented by the equation $y-5=3\left(x-2\right)$ .