QuestionFind the function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ . Options: $x+4y=12$ , $\frac{2}{3}x+3y=-3$ , $6x-7y=21$ , $-\frac{2}{3}x+3y=6$ .

Studdy Solution

STEP 1

Assumptions1. The y-intercept of a function is the point where the line crosses the y-axis. This is when x =0. . The given functions are linear equations in two variables, x and y.

STEP 2

First, we need to find the y-intercept of the given function. We can do this by setting x =0 in the equation.
$y = \frac{2}{}x -$

STEP 3

Now, plug in x =0 into the equation to calculate the y-intercept.
$y = \frac{2}{3}(0) -3$

STEP 4

Calculate the y-intercept of the given function.
$y = -3$

STEP 5

Now, we need to find the y-intercept of each of the other functions. We can do this by setting x =0 in each equation and solving for y.
For the function $x +4y =12$ , when x =0, we have $4y =12$

STEP 6

olve for y to find the y-intercept of the function $x +4y =12$ .
$y = \frac{12}{4} =3$

STEP 7

For the function $\frac{2}{3}x +3y = -3$ , when x =0, we have $3y = -3$

STEP 8

olve for y to find the y-intercept of the function $\frac{2}{3}x +3y = -3$ .
$y = \frac{-3}{3} = -1$

STEP 9

For the function $6x -7y =21$ , when x =, we have $-7y =21$

STEP 10

olve for y to find the y-intercept of the function $6x -7y =21$ .
$y = \frac{21}{-7} = -3$

STEP 11

For the function $-\frac{}{3}x +3y =6$ , when x =0, we have $3y =6$

STEP 12

olve for y to find the y-intercept of the function $-\frac{2}{}x +y =6$ .
$y = \frac{6}{} =2$

STEP 13

Now that we have the y-intercepts of all the functions, we can compare them to the y-intercept of the given function. The function with the same y-intercept as the given function is the one that has y-intercept -3.
The function $6x -7y =21$ has the same y-intercept as the given function $y = \frac{2}{3}x -3$ .

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QuestionFind the function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ . Options: $x+4y=12$ , $\frac{2}{3}x+3y=-3$ , $6x-7y=21$ , $-\frac{2}{3}x+3y=6$ .

Studdy Solution

STEP 1

Assumptions1. The y-intercept of a function is the point where the line crosses the y-axis. This is when x =0. . The given functions are linear equations in two variables, x and y.

STEP 2

First, we need to find the y-intercept of the given function. We can do this by setting x =0 in the equation.
$y = \frac{2}{}x -$

STEP 3

Now, plug in x =0 into the equation to calculate the y-intercept.
$y = \frac{2}{3}(0) -3$

STEP 4

Calculate the y-intercept of the given function.
$y = -3$

STEP 5

Now, we need to find the y-intercept of each of the other functions. We can do this by setting x =0 in each equation and solving for y.
For the function $x +4y =12$ , when x =0, we have $4y =12$

STEP 6

olve for y to find the y-intercept of the function $x +4y =12$ .
$y = \frac{12}{4} =3$

STEP 7

For the function $\frac{2}{3}x +3y = -3$ , when x =0, we have $3y = -3$

STEP 8

olve for y to find the y-intercept of the function $\frac{2}{3}x +3y = -3$ .
$y = \frac{-3}{3} = -1$

STEP 9

For the function $6x -7y =21$ , when x =, we have $-7y =21$

STEP 10

olve for y to find the y-intercept of the function $6x -7y =21$ .
$y = \frac{21}{-7} = -3$

STEP 11

For the function $-\frac{}{3}x +3y =6$ , when x =0, we have $3y =6$

STEP 12

olve for y to find the y-intercept of the function $-\frac{2}{}x +y =6$ .
$y = \frac{6}{} =2$

STEP 13

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QuestionFind the function with the same yyy-intercept as y=23x−3y=\frac{2}{3} x-3y=32​x−3. Options: x+4y=12x+4y=12x+4y=12, 23x+3y=−3\frac{2}{3}x+3y=-332​x+3y=−3, 6x−7y=216x-7y=216x−7y=21, −23x+3y=6-\frac{2}{3}x+3y=6−32​x+3y=6.

Studdy Solution

STEP 1

Assumptions1. The y-intercept of a function is the point where the line crosses the y-axis. This is when x =0. . The given functions are linear equations in two variables, x and y.

STEP 2

First, we need to find the y-intercept of the given function. We can do this by setting x =0 in the equation.y=2x−y = \frac{2}{}x -y=2​x−

STEP 3

Now, plug in x =0 into the equation to calculate the y-intercept.y=23(0)−3y = \frac{2}{3}(0) -3y=32​(0)−3

STEP 4

Calculate the y-intercept of the given function.y=−3y = -3y=−3

STEP 5

Now, we need to find the y-intercept of each of the other functions. We can do this by setting x =0 in each equation and solving for y.For the function x+4y=12x +4y =12x+4y=12, when x =0, we have4y=124y =124y=12

STEP 6

olve for y to find the y-intercept of the function x+4y=12x +4y =12x+4y=12.y=124=3y = \frac{12}{4} =3y=412​=3

STEP 7

For the function 23x+3y=−3\frac{2}{3}x +3y = -332​x+3y=−3, when x =0, we have3y=−33y = -33y=−3

STEP 8

olve for y to find the y-intercept of the function 23x+3y=−3\frac{2}{3}x +3y = -332​x+3y=−3.y=−33=−1y = \frac{-3}{3} = -1y=3−3​=−1

STEP 9

For the function 6x−7y=216x -7y =216x−7y=21, when x =, we have−7y=21-7y =21−7y=21

STEP 10

olve for y to find the y-intercept of the function 6x−7y=216x -7y =216x−7y=21.y=21−7=−3y = \frac{21}{-7} = -3y=−721​=−3

STEP 11

For the function −3x+3y=6-\frac{}{3}x +3y =6−3​x+3y=6, when x =0, we have3y=63y =63y=6

STEP 12

olve for y to find the y-intercept of the function −2x+y=6-\frac{2}{}x +y =6−2​x+y=6.y=6=2y = \frac{6}{} =2y=6​=2

STEP 13

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QuestionFind the function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ . Options: $x+4y=12$ , $\frac{2}{3}x+3y=-3$ , $6x-7y=21$ , $-\frac{2}{3}x+3y=6$ .

First, we need to find the y-intercept of the given function. We can do this by setting x =0 in the equation.
$y = \frac{2}{}x -$

Now, plug in x =0 into the equation to calculate the y-intercept.
$y = \frac{2}{3}(0) -3$

Calculate the y-intercept of the given function.
$y = -3$

Now, we need to find the y-intercept of each of the other functions. We can do this by setting x =0 in each equation and solving for y.
For the function $x +4y =12$ , when x =0, we have $4y =12$

olve for y to find the y-intercept of the function $x +4y =12$ .
$y = \frac{12}{4} =3$

For the function $\frac{2}{3}x +3y = -3$ , when x =0, we have $3y = -3$

olve for y to find the y-intercept of the function $\frac{2}{3}x +3y = -3$ .
$y = \frac{-3}{3} = -1$

For the function $6x -7y =21$ , when x =, we have $-7y =21$

olve for y to find the y-intercept of the function $6x -7y =21$ .
$y = \frac{21}{-7} = -3$

For the function $-\frac{}{3}x +3y =6$ , when x =0, we have $3y =6$

olve for y to find the y-intercept of the function $-\frac{2}{}x +y =6$ .
$y = \frac{6}{} =2$