QuestionCari nilai $k$ agar garis $x-1+k y=0$ selari dengan garis $\frac{x}{3}+\frac{y}{4}=1$ .

Studdy Solution

STEP 1

Assumptions1. The given straight line is $x-1+ky=0$ . The line it is parallel to is $\frac{x}{3}+\frac{y}{4}=1$
3. Two lines are parallel if and only if their slopes are equal

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a line is $y = mx + c$ , where $m$ is the slope. So, we need to rearrange the equation $x-1+ky=0$ to this form.
$ky = -x +1$

STEP 3

Divide both sides of the equation by $k$ to isolate $y$ .
$y = -\frac{1}{k}x + \frac{1}{k}$

STEP 4

Now, we can see that the slope of the given line is $-\frac{1}{k}$ .

STEP 5

Next, we need to find the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ . Again, we need to rearrange this equation to the slope-intercept form.
$\frac{y}{4} = -\frac{x}{3} +1$

STEP 6

Multiply both sides of the equation by4 to isolate $y$ .
$y = -\frac{4}{3}x +4$

STEP 7

Now, we can see that the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ is $-\frac{4}{3}$ .

STEP 8

Since the two lines are parallel, their slopes are equal. Therefore, we can set the two slopes equal to each other and solve for $k$ .
$-\frac{1}{k} = -\frac{4}{3}$

STEP 9

Multiply both sides of the equation by $-$ to get rid of the negative sign.
$\frac{}{k} = \frac{4}{3}$

STEP 10

Finally, solve for $k$ by taking the reciprocal of both sides.
$k = \frac{3}{4}$ So, the value of $k$ is $\frac{3}{4}$ .

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QuestionCari nilai $k$ agar garis $x-1+k y=0$ selari dengan garis $\frac{x}{3}+\frac{y}{4}=1$ .

Studdy Solution

STEP 1

Assumptions1. The given straight line is $x-1+ky=0$ . The line it is parallel to is $\frac{x}{3}+\frac{y}{4}=1$
3. Two lines are parallel if and only if their slopes are equal

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a line is $y = mx + c$ , where $m$ is the slope. So, we need to rearrange the equation $x-1+ky=0$ to this form.
$ky = -x +1$

STEP 3

Divide both sides of the equation by $k$ to isolate $y$ .
$y = -\frac{1}{k}x + \frac{1}{k}$

STEP 4

Now, we can see that the slope of the given line is $-\frac{1}{k}$ .

STEP 5

Next, we need to find the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ . Again, we need to rearrange this equation to the slope-intercept form.
$\frac{y}{4} = -\frac{x}{3} +1$

STEP 6

Multiply both sides of the equation by4 to isolate $y$ .
$y = -\frac{4}{3}x +4$

STEP 7

Now, we can see that the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ is $-\frac{4}{3}$ .

STEP 8

Since the two lines are parallel, their slopes are equal. Therefore, we can set the two slopes equal to each other and solve for $k$ .
$-\frac{1}{k} = -\frac{4}{3}$

STEP 9

Multiply both sides of the equation by $-$ to get rid of the negative sign.
$\frac{}{k} = \frac{4}{3}$

STEP 10

Finally, solve for $k$ by taking the reciprocal of both sides.
$k = \frac{3}{4}$ So, the value of $k$ is $\frac{3}{4}$ .

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QuestionCari nilai kkk agar garis x−1+ky=0x-1+k y=0x−1+ky=0 selari dengan garis x3+y4=1\frac{x}{3}+\frac{y}{4}=13x​+4y​=1.

Studdy Solution

STEP 1

Assumptions1. The given straight line is x−1+ky=0x-1+ky=0x−1+ky=0 . The line it is parallel to is x3+y4=1\frac{x}{3}+\frac{y}{4}=13x​+4y​=13. Two lines are parallel if and only if their slopes are equal

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a line is y=mx+cy = mx + cy=mx+c, where mmm is the slope. So, we need to rearrange the equation x−1+ky=0x-1+ky=0x−1+ky=0 to this form.ky=−x+1ky = -x +1ky=−x+1

STEP 3

Divide both sides of the equation by kkk to isolate yyy.y=−1kx+1ky = -\frac{1}{k}x + \frac{1}{k}y=−k1​x+k1​

STEP 4

Now, we can see that the slope of the given line is −1k-\frac{1}{k}−k1​.

STEP 5

Next, we need to find the slope of the line x3+y4=1\frac{x}{3}+\frac{y}{4}=13x​+4y​=1. Again, we need to rearrange this equation to the slope-intercept form.y4=−x3+1\frac{y}{4} = -\frac{x}{3} +14y​=−3x​+1

STEP 6

Multiply both sides of the equation by4 to isolate yyy.y=−43x+4y = -\frac{4}{3}x +4y=−34​x+4

STEP 7

Now, we can see that the slope of the line x3+y4=1\frac{x}{3}+\frac{y}{4}=13x​+4y​=1 is −43-\frac{4}{3}−34​.

STEP 8

Since the two lines are parallel, their slopes are equal. Therefore, we can set the two slopes equal to each other and solve for kkk.−1k=−43-\frac{1}{k} = -\frac{4}{3}−k1​=−34​

STEP 9

Multiply both sides of the equation by −-− to get rid of the negative sign.k=43\frac{}{k} = \frac{4}{3}k​=34​

STEP 10

Finally, solve for kkk by taking the reciprocal of both sides.k=34k = \frac{3}{4}k=43​So, the value of kkk is 34\frac{3}{4}43​.

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QuestionCari nilai $k$ agar garis $x-1+k y=0$ selari dengan garis $\frac{x}{3}+\frac{y}{4}=1$ .

Assumptions1. The given straight line is $x-1+ky=0$ . The line it is parallel to is $\frac{x}{3}+\frac{y}{4}=1$
3. Two lines are parallel if and only if their slopes are equal

First, we need to find the slope of the given line. The slope-intercept form of a line is $y = mx + c$ , where $m$ is the slope. So, we need to rearrange the equation $x-1+ky=0$ to this form.
$ky = -x +1$

Divide both sides of the equation by $k$ to isolate $y$ .
$y = -\frac{1}{k}x + \frac{1}{k}$

Now, we can see that the slope of the given line is $-\frac{1}{k}$ .

Next, we need to find the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ . Again, we need to rearrange this equation to the slope-intercept form.
$\frac{y}{4} = -\frac{x}{3} +1$

Multiply both sides of the equation by4 to isolate $y$ .
$y = -\frac{4}{3}x +4$

Now, we can see that the slope of the line $\frac{x}{3}+\frac{y}{4}=1$ is $-\frac{4}{3}$ .

Since the two lines are parallel, their slopes are equal. Therefore, we can set the two slopes equal to each other and solve for $k$ .
$-\frac{1}{k} = -\frac{4}{3}$

Multiply both sides of the equation by $-$ to get rid of the negative sign.
$\frac{}{k} = \frac{4}{3}$

Finally, solve for $k$ by taking the reciprocal of both sides.
$k = \frac{3}{4}$ So, the value of $k$ is $\frac{3}{4}$ .