QuestionWrite the line equation in point-slope and slope-intercept forms with slope $=-7$ and passing through $(-8,-3)$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the line is $-7$ . . The line passes through the point $(-8,-3)$ .

STEP 2

The point-slope form of a line is given by the formula $y - y1 = m(x - x1)$ where $m$ is the slope of the line, and $(x1, y1)$ is a point on the line.

STEP 3

Substitute the given slope and point into the point-slope form equation.
$y - (-3) = -7(x - (-8))$

STEP 4

implify the equation by removing the double negatives.
$y +3 = -7(x +8)$ This is the equation of the line in point-slope form.

STEP 5

To find the equation of the line in slope-intercept form, we need to convert the point-slope form into the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 6

istribute the $-$ on the right side of the equation.
$y +3 = -x -56$

STEP 7

Subtract $3$ from both sides to isolate $y$ .
$y = -7x -56 -3$

STEP 8

implify the equation.
$y = -7x -59$ This is the equation of the line in slope-intercept form.

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QuestionWrite the line equation in point-slope and slope-intercept forms with slope $=-7$ and passing through $(-8,-3)$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the line is $-7$ . . The line passes through the point $(-8,-3)$ .

STEP 2

The point-slope form of a line is given by the formula $y - y1 = m(x - x1)$ where $m$ is the slope of the line, and $(x1, y1)$ is a point on the line.

STEP 3

Substitute the given slope and point into the point-slope form equation.
$y - (-3) = -7(x - (-8))$

STEP 4

implify the equation by removing the double negatives.
$y +3 = -7(x +8)$ This is the equation of the line in point-slope form.

STEP 5

To find the equation of the line in slope-intercept form, we need to convert the point-slope form into the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 6

istribute the $-$ on the right side of the equation.
$y +3 = -x -56$

STEP 7

Subtract $3$ from both sides to isolate $y$ .
$y = -7x -56 -3$

STEP 8

implify the equation.
$y = -7x -59$ This is the equation of the line in slope-intercept form.

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QuestionWrite the line equation in point-slope and slope-intercept forms with slope =−7=-7=−7 and passing through (−8,−3)(-8,-3)(−8,−3).

Studdy Solution

STEP 1

Assumptions1. The slope of the line is −7-7−7. . The line passes through the point (−8,−3)(-8,-3)(−8,−3).

STEP 2

The point-slope form of a line is given by the formulay−y1=m(x−x1)y - y1 = m(x - x1)y−y1=m(x−x1)where mmm is the slope of the line, and (x1,y1)(x1, y1)(x1,y1) is a point on the line.

STEP 3

Substitute the given slope and point into the point-slope form equation.y−(−3)=−7(x−(−8))y - (-3) = -7(x - (-8))y−(−3)=−7(x−(−8))

STEP 4

implify the equation by removing the double negatives.y+3=−7(x+8)y +3 = -7(x +8)y+3=−7(x+8)This is the equation of the line in point-slope form.

STEP 5

To find the equation of the line in slope-intercept form, we need to convert the point-slope form into the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 6

istribute the −-− on the right side of the equation.y+3=−x−56y +3 = -x -56y+3=−x−56

STEP 7

Subtract 333 from both sides to isolate yyy.y=−7x−56−3y = -7x -56 -3y=−7x−56−3

STEP 8

implify the equation.y=−7x−59y = -7x -59y=−7x−59This is the equation of the line in slope-intercept form.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWrite the line equation in point-slope and slope-intercept forms with slope $=-7$ and passing through $(-8,-3)$ .

Assumptions1. The slope of the line is $-7$ . . The line passes through the point $(-8,-3)$ .

The point-slope form of a line is given by the formula $y - y1 = m(x - x1)$ where $m$ is the slope of the line, and $(x1, y1)$ is a point on the line.

Substitute the given slope and point into the point-slope form equation.
$y - (-3) = -7(x - (-8))$

implify the equation by removing the double negatives.
$y +3 = -7(x +8)$ This is the equation of the line in point-slope form.

To find the equation of the line in slope-intercept form, we need to convert the point-slope form into the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

istribute the $-$ on the right side of the equation.
$y +3 = -x -56$

Subtract $3$ from both sides to isolate $y$ .
$y = -7x -56 -3$

implify the equation.
$y = -7x -59$ This is the equation of the line in slope-intercept form.