QuestionFind the slope of the line given by the equation $2x + 3y = 12$ .

Studdy Solution

STEP 1

Assumptions1. We are given a point $(3,1)$ . We are given a linear equation $x +3y =12$
3. We need to find the slope of the line represented by the equation

STEP 2

The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We need to rewrite the given equation in this form to find the slope.
$2x +y =12$

STEP 3

Subtract $2x$ from both sides of the equation to isolate $y$ on one side.
$3y = -2x +12$

STEP 4

Divide all terms by $3$ to get $y$ by itself.
$y = -\frac{2}{3}x +4$

STEP 5

Now that we have the equation in slope-intercept form, we can see that the slope $m$ is $-\frac{2}{3}$ .
So, the slope of the line represented by the equation $2x +3y =12$ is $-\frac{2}{3}$ .

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QuestionFind the slope of the line given by the equation $2x + 3y = 12$ .

Studdy Solution

STEP 1

Assumptions1. We are given a point $(3,1)$ . We are given a linear equation $x +3y =12$
3. We need to find the slope of the line represented by the equation

STEP 2

The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We need to rewrite the given equation in this form to find the slope.
$2x +y =12$

STEP 3

Subtract $2x$ from both sides of the equation to isolate $y$ on one side.
$3y = -2x +12$

STEP 4

Divide all terms by $3$ to get $y$ by itself.
$y = -\frac{2}{3}x +4$

STEP 5

Now that we have the equation in slope-intercept form, we can see that the slope $m$ is $-\frac{2}{3}$ .
So, the slope of the line represented by the equation $2x +3y =12$ is $-\frac{2}{3}$ .

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QuestionFind the slope of the line given by the equation 2x+3y=122x + 3y = 122x+3y=12.

Studdy Solution

STEP 1

Assumptions1. We are given a point (3,1)(3,1)(3,1). We are given a linear equation x+3y=12x +3y =12x+3y=123. We need to find the slope of the line represented by the equation

STEP 2

The slope-intercept form of a linear equation is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept. We need to rewrite the given equation in this form to find the slope.2x+y=122x +y =122x+y=12

STEP 3

Subtract 2x2x2x from both sides of the equation to isolate yyy on one side.3y=−2x+123y = -2x +123y=−2x+12

STEP 4

Divide all terms by 333 to get yyy by itself.y=−23x+4y = -\frac{2}{3}x +4y=−32​x+4

STEP 5

Now that we have the equation in slope-intercept form, we can see that the slope mmm is −23-\frac{2}{3}−32​.So, the slope of the line represented by the equation 2x+3y=122x +3y =122x+3y=12 is −23-\frac{2}{3}−32​.

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QuestionFind the slope of the line given by the equation $2x + 3y = 12$ .

Assumptions1. We are given a point $(3,1)$ . We are given a linear equation $x +3y =12$
3. We need to find the slope of the line represented by the equation

The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We need to rewrite the given equation in this form to find the slope.
$2x +y =12$

Subtract $2x$ from both sides of the equation to isolate $y$ on one side.
$3y = -2x +12$

Divide all terms by $3$ to get $y$ by itself.
$y = -\frac{2}{3}x +4$

Now that we have the equation in slope-intercept form, we can see that the slope $m$ is $-\frac{2}{3}$ .
So, the slope of the line represented by the equation $2x +3y =12$ is $-\frac{2}{3}$ .