QuestionFind the line equation with slope -2 passing through the point $(4,-7)$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the line is -. The line passes through the point (4,-7)

STEP 2

The equation of a line in slope-intercept form is given by $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

STEP 3

We know the slope $m$ is -2, so we can substitute this into the equation.
$y = -2x + b$

STEP 4

To find the y-intercept $b$ , we can substitute the coordinates of the known point (4,-7) into the equation.
$-7 = -2(4) + b$

STEP 5

implify the equation to solve for $b$ .
$-7 = -8 + b$

STEP 6

Rearrange the equation to solve for $b$ .
$b = - +8$

STEP 7

Calculate the value of $b$ .
$b =1$

STEP 8

Now that we have the value of $b$ , we can substitute this back into the equation to get the final equation of the line.
$y = -2x +1$ The equation of the line that has a slope of -2 and goes through the point $(4,-7)$ is $y = -2x +1$ .

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QuestionFind the line equation with slope -2 passing through the point $(4,-7)$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the line is -. The line passes through the point (4,-7)

STEP 2

The equation of a line in slope-intercept form is given by $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

STEP 3

We know the slope $m$ is -2, so we can substitute this into the equation.
$y = -2x + b$

STEP 4

To find the y-intercept $b$ , we can substitute the coordinates of the known point (4,-7) into the equation.
$-7 = -2(4) + b$

STEP 5

implify the equation to solve for $b$ .
$-7 = -8 + b$

STEP 6

Rearrange the equation to solve for $b$ .
$b = - +8$

STEP 7

Calculate the value of $b$ .
$b =1$

STEP 8

Now that we have the value of $b$ , we can substitute this back into the equation to get the final equation of the line.
$y = -2x +1$ The equation of the line that has a slope of -2 and goes through the point $(4,-7)$ is $y = -2x +1$ .

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QuestionFind the line equation with slope -2 passing through the point (4,−7)(4,-7)(4,−7).

Studdy Solution

STEP 1

Assumptions1. The slope of the line is -. The line passes through the point (4,-7)

STEP 2

The equation of a line in slope-intercept form is given byy=mx+by = mx + by=mx+bwhere mmm is the slope and bbb is the y-intercept.

STEP 3

We know the slope mmm is -2, so we can substitute this into the equation.y=−2x+by = -2x + by=−2x+b

STEP 4

To find the y-intercept bbb, we can substitute the coordinates of the known point (4,-7) into the equation.−7=−2(4)+b-7 = -2(4) + b−7=−2(4)+b

STEP 5

implify the equation to solve for bbb.−7=−8+b-7 = -8 + b−7=−8+b

STEP 6

Rearrange the equation to solve for bbb.b=−+8b = - +8b=−+8

STEP 7

Calculate the value of bbb.b=1b =1b=1

STEP 8

Now that we have the value of bbb, we can substitute this back into the equation to get the final equation of the line.y=−2x+1y = -2x +1y=−2x+1The equation of the line that has a slope of -2 and goes through the point (4,−7)(4,-7)(4,−7) is y=−2x+1y = -2x +1y=−2x+1.

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QuestionFind the line equation with slope -2 passing through the point $(4,-7)$ .

The equation of a line in slope-intercept form is given by $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

We know the slope $m$ is -2, so we can substitute this into the equation.
$y = -2x + b$

To find the y-intercept $b$ , we can substitute the coordinates of the known point (4,-7) into the equation.
$-7 = -2(4) + b$

implify the equation to solve for $b$ .
$-7 = -8 + b$

Rearrange the equation to solve for $b$ .
$b = - +8$

Calculate the value of $b$ .
$b =1$

Now that we have the value of $b$ , we can substitute this back into the equation to get the final equation of the line.
$y = -2x +1$ The equation of the line that has a slope of -2 and goes through the point $(4,-7)$ is $y = -2x +1$ .