QuestionFind the standard form equation of the line through points $(0,6)$ and $(4,0)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two points $(0,6)$ and $(4,0)$ . We are to find the equation of the line in standard form that passes through these points

STEP 2

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Substitute the given points into the slope formula $m = \frac{0 -6}{ -0}$

STEP 4

Calculate the slope $m = \frac{-6}{4} = -\frac{3}{2}$

STEP 5

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 6

Substitute the calculated slope and the point $(0,6)$ (which gives us the y-intercept) into the slope-intercept form $y = -\frac{3}{2}x +6$

STEP 7

To convert the equation from slope-intercept form to standard form, we want to eliminate the fractions and have the x and y terms on the left side of the equation. Multiply every term by2 to eliminate the fraction $2y = -3x +12$

STEP 8

Rearrange the equation to standard form (Ax + By = C):
$3x +2y =12$ This is the equation of the line in standard form that passes through the points $(0,6)$ and $(4,0)$ .

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QuestionFind the standard form equation of the line through points $(0,6)$ and $(4,0)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two points $(0,6)$ and $(4,0)$ . We are to find the equation of the line in standard form that passes through these points

STEP 2

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Substitute the given points into the slope formula $m = \frac{0 -6}{ -0}$

STEP 4

Calculate the slope $m = \frac{-6}{4} = -\frac{3}{2}$

STEP 5

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 6

Substitute the calculated slope and the point $(0,6)$ (which gives us the y-intercept) into the slope-intercept form $y = -\frac{3}{2}x +6$

STEP 7

To convert the equation from slope-intercept form to standard form, we want to eliminate the fractions and have the x and y terms on the left side of the equation. Multiply every term by2 to eliminate the fraction $2y = -3x +12$

STEP 8

Rearrange the equation to standard form (Ax + By = C):
$3x +2y =12$ This is the equation of the line in standard form that passes through the points $(0,6)$ and $(4,0)$ .

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QuestionFind the standard form equation of the line through points (0,6)(0,6)(0,6) and (4,0)(4,0)(4,0).

Studdy Solution

STEP 1

Assumptions1. We are given two points (0,6)(0,6)(0,6) and (4,0)(4,0)(4,0). We are to find the equation of the line in standard form that passes through these points

STEP 2

The slope of a line passing through two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Substitute the given points into the slope formulam=0−6−0m = \frac{0 -6}{ -0}m=−00−6​

STEP 4

Calculate the slopem=−64=−32m = \frac{-6}{4} = -\frac{3}{2}m=4−6​=−23​

STEP 5

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

STEP 6

Substitute the calculated slope and the point (0,6)(0,6)(0,6) (which gives us the y-intercept) into the slope-intercept formy=−32x+6y = -\frac{3}{2}x +6y=−23​x+6

STEP 7

To convert the equation from slope-intercept form to standard form, we want to eliminate the fractions and have the x and y terms on the left side of the equation. Multiply every term by2 to eliminate the fraction2y=−3x+122y = -3x +122y=−3x+12

STEP 8

Rearrange the equation to standard form (Ax + By = C):3x+2y=123x +2y =123x+2y=12This is the equation of the line in standard form that passes through the points (0,6)(0,6)(0,6) and (4,0)(4,0)(4,0).

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QuestionFind the standard form equation of the line through points $(0,6)$ and $(4,0)$ .

Assumptions1. We are given two points $(0,6)$ and $(4,0)$ . We are to find the equation of the line in standard form that passes through these points

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Substitute the given points into the slope formula $m = \frac{0 -6}{ -0}$

Calculate the slope $m = \frac{-6}{4} = -\frac{3}{2}$

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.

Substitute the calculated slope and the point $(0,6)$ (which gives us the y-intercept) into the slope-intercept form $y = -\frac{3}{2}x +6$

To convert the equation from slope-intercept form to standard form, we want to eliminate the fractions and have the x and y terms on the left side of the equation. Multiply every term by2 to eliminate the fraction $2y = -3x +12$

Rearrange the equation to standard form (Ax + By = C):
$3x +2y =12$ This is the equation of the line in standard form that passes through the points $(0,6)$ and $(4,0)$ .