QuestionFind the standard form equation of the line through points $(8,3)$ and $(-4,7)$ .

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian plane $(8,3)$ and $(-4,7)$ . . We need to find the equation of the line passing through these points.
3. The standard form of the line equation is $Ax + By = C$ , where $A$ , $B$ , and $C$ are integers, and $A$ and $B$ are not both zero.

STEP 2

First, we need to find the slope of the line. The slope ( $m$ ) is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{7 -3}{- -8}$

STEP 4

Calculate the slope.
$m = \frac{4}{-12} = -\frac{1}{3}$

STEP 5

Now that we have the slope, we can use the point-slope form of the line equation to write an equation for the line. The point-slope form is $y - y1 = m(x - x1)$ .

STEP 6

Plug in the values for $m$ , $x1$ , and $y1$ to write the equation of the line.
$y -3 = -\frac{1}{3}(x -8)$

STEP 7

istribute the $-\frac{1}{3}$ on the right side of the equation.
$y -3 = -\frac{1}{3}x + \frac{}{3}$

STEP 8

To write the equation in standard form, we want to eliminate the fractions and move all terms to one side of the equation. First, multiply every term by3 to eliminate the fractions.
$3y - = -x +8$

STEP 9

Finally, rearrange the terms to get the equation in standard form.
$x +3y =17$ This is the equation of the line in standard form.

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QuestionFind the standard form equation of the line through points $(8,3)$ and $(-4,7)$ .

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian plane $(8,3)$ and $(-4,7)$ . . We need to find the equation of the line passing through these points.
3. The standard form of the line equation is $Ax + By = C$ , where $A$ , $B$ , and $C$ are integers, and $A$ and $B$ are not both zero.

STEP 2

First, we need to find the slope of the line. The slope ( $m$ ) is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{7 -3}{- -8}$

STEP 4

Calculate the slope.
$m = \frac{4}{-12} = -\frac{1}{3}$

STEP 5

Now that we have the slope, we can use the point-slope form of the line equation to write an equation for the line. The point-slope form is $y - y1 = m(x - x1)$ .

STEP 6

Plug in the values for $m$ , $x1$ , and $y1$ to write the equation of the line.
$y -3 = -\frac{1}{3}(x -8)$

STEP 7

istribute the $-\frac{1}{3}$ on the right side of the equation.
$y -3 = -\frac{1}{3}x + \frac{}{3}$

STEP 8

To write the equation in standard form, we want to eliminate the fractions and move all terms to one side of the equation. First, multiply every term by3 to eliminate the fractions.
$3y - = -x +8$

STEP 9

Finally, rearrange the terms to get the equation in standard form.
$x +3y =17$ This is the equation of the line in standard form.

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QuestionFind the standard form equation of the line through points (8,3)(8,3)(8,3) and (−4,7)(-4,7)(−4,7).

Studdy Solution

STEP 1

STEP 2

First, we need to find the slope of the line. The slope (mmm) is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Now, plug in the given values for x1x1x1, y1y1y1, x2x2x2, and y2y2y2 to calculate the slope.m=7−3−−8m = \frac{7 -3}{- -8}m=−−87−3​

STEP 4

Calculate the slope.m=4−12=−13m = \frac{4}{-12} = -\frac{1}{3}m=−124​=−31​

STEP 5

Now that we have the slope, we can use the point-slope form of the line equation to write an equation for the line. The point-slope form is y−y1=m(x−x1)y - y1 = m(x - x1)y−y1=m(x−x1).

STEP 6

Plug in the values for mmm, x1x1x1, and y1y1y1 to write the equation of the line.y−3=−13(x−8)y -3 = -\frac{1}{3}(x -8)y−3=−31​(x−8)

STEP 7

istribute the −13-\frac{1}{3}−31​ on the right side of the equation.y−3=−13x+3y -3 = -\frac{1}{3}x + \frac{}{3}y−3=−31​x+3​

STEP 8

To write the equation in standard form, we want to eliminate the fractions and move all terms to one side of the equation. First, multiply every term by3 to eliminate the fractions.3y−=−x+83y - = -x +83y−=−x+8

STEP 9

Finally, rearrange the terms to get the equation in standard form.x+3y=17x +3y =17x+3y=17This is the equation of the line in standard form.

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QuestionFind the standard form equation of the line through points $(8,3)$ and $(-4,7)$ .

First, we need to find the slope of the line. The slope ( $m$ ) is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{7 -3}{- -8}$

Calculate the slope.
$m = \frac{4}{-12} = -\frac{1}{3}$

Now that we have the slope, we can use the point-slope form of the line equation to write an equation for the line. The point-slope form is $y - y1 = m(x - x1)$ .

Plug in the values for $m$ , $x1$ , and $y1$ to write the equation of the line.
$y -3 = -\frac{1}{3}(x -8)$

istribute the $-\frac{1}{3}$ on the right side of the equation.
$y -3 = -\frac{1}{3}x + \frac{}{3}$

To write the equation in standard form, we want to eliminate the fractions and move all terms to one side of the equation. First, multiply every term by3 to eliminate the fractions.
$3y - = -x +8$

Finally, rearrange the terms to get the equation in standard form.
$x +3y =17$ This is the equation of the line in standard form.