Math / Algebra

Question6. MJ is creating a graph of the equation $2 x+4 y=-8$ . Which of the following points will lie on the line? a. $(2,4)$ b. $(-2,-1)$ c. $(2,1)$ d. $(4,4)$

Studdy Solution

STEP 1

Assumptions
1. The equation of the line is given as $2x + 4y = -8$ .
2. We need to determine which of the given points lie on this line.
3. The points to be tested are: a. $(2, 4)$ b. $(-2, -1)$ c. $(2, 1)$ d. $(4, 4)$

STEP 2

To determine if a point lies on the line, substitute the $x$ and $y$ values of the point into the equation $2x + 4y = -8$ . If the equation holds true, then the point lies on the line.

STEP 3

Test point $(2, 4)$ .
Substitute $x = 2$ and $y = 4$ into the equation:
$2(2) + 4(4) = -8$

STEP 4

Calculate the left side of the equation for point $(2, 4)$ :
$4 + 16 = 20$
Since $20 \neq -8$ , point $(2, 4)$ does not lie on the line.

STEP 5

Test point $(-2, -1)$ .
Substitute $x = -2$ and $y = -1$ into the equation:
$2(-2) + 4(-1) = -8$

STEP 6

Calculate the left side of the equation for point $(-2, -1)$ :
$-4 - 4 = -8$
Since $-8 = -8$ , point $(-2, -1)$ lies on the line.

STEP 7

Test point $(2, 1)$ .
Substitute $x = 2$ and $y = 1$ into the equation:
$2(2) + 4(1) = -8$

STEP 8

Calculate the left side of the equation for point $(2, 1)$ :
$4 + 4 = 8$
Since $8 \neq -8$ , point $(2, 1)$ does not lie on the line.

STEP 9

Test point $(4, 4)$ .
Substitute $x = 4$ and $y = 4$ into the equation:
$2(4) + 4(4) = -8$

STEP 10

Calculate the left side of the equation for point $(4, 4)$ :
$8 + 16 = 24$
Since $24 \neq -8$ , point $(4, 4)$ does not lie on the line.

STEP 11

Conclusion: The only point that lies on the line $2x + 4y = -8$ is $(-2, -1)$ .

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Question6. MJ is creating a graph of the equation $2 x+4 y=-8$ . Which of the following points will lie on the line? a. $(2,4)$ b. $(-2,-1)$ c. $(2,1)$ d. $(4,4)$

Studdy Solution

STEP 1

Assumptions
1. The equation of the line is given as $2x + 4y = -8$ .
2. We need to determine which of the given points lie on this line.
3. The points to be tested are: a. $(2, 4)$ b. $(-2, -1)$ c. $(2, 1)$ d. $(4, 4)$

STEP 2

To determine if a point lies on the line, substitute the $x$ and $y$ values of the point into the equation $2x + 4y = -8$ . If the equation holds true, then the point lies on the line.

STEP 3

Test point $(2, 4)$ .
Substitute $x = 2$ and $y = 4$ into the equation:
$2(2) + 4(4) = -8$

STEP 4

Calculate the left side of the equation for point $(2, 4)$ :
$4 + 16 = 20$
Since $20 \neq -8$ , point $(2, 4)$ does not lie on the line.

STEP 5

Test point $(-2, -1)$ .
Substitute $x = -2$ and $y = -1$ into the equation:
$2(-2) + 4(-1) = -8$

STEP 6

Calculate the left side of the equation for point $(-2, -1)$ :
$-4 - 4 = -8$
Since $-8 = -8$ , point $(-2, -1)$ lies on the line.

STEP 7

Test point $(2, 1)$ .
Substitute $x = 2$ and $y = 1$ into the equation:
$2(2) + 4(1) = -8$

STEP 8

Calculate the left side of the equation for point $(2, 1)$ :
$4 + 4 = 8$
Since $8 \neq -8$ , point $(2, 1)$ does not lie on the line.

STEP 9

Test point $(4, 4)$ .
Substitute $x = 4$ and $y = 4$ into the equation:
$2(4) + 4(4) = -8$

STEP 10

Calculate the left side of the equation for point $(4, 4)$ :
$8 + 16 = 24$
Since $24 \neq -8$ , point $(4, 4)$ does not lie on the line.

STEP 11

Conclusion: The only point that lies on the line $2x + 4y = -8$ is $(-2, -1)$ .

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Question6. MJ is creating a graph of the equation 2x+4y=−82 x+4 y=-82x+4y=−8. Which of the following points will lie on the line? a. (2,4)(2,4)(2,4) b. (−2,−1)(-2,-1)(−2,−1) c. (2,1)(2,1)(2,1) d. (4,4)(4,4)(4,4)

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as 2x+4y=−82x + 4y = -82x+4y=−8.2. We need to determine which of the given points lie on this line.3. The points to be tested are: a. (2,4)(2, 4)(2,4) b. (−2,−1)(-2, -1)(−2,−1) c. (2,1)(2, 1)(2,1) d. (4,4)(4, 4)(4,4)

STEP 2

To determine if a point lies on the line, substitute the xxx and yyy values of the point into the equation 2x+4y=−82x + 4y = -82x+4y=−8. If the equation holds true, then the point lies on the line.

STEP 3

Test point (2,4)(2, 4)(2,4).Substitute x=2x = 2x=2 and y=4y = 4y=4 into the equation:2(2)+4(4)=−82(2) + 4(4) = -82(2)+4(4)=−8

STEP 4

Calculate the left side of the equation for point (2,4)(2, 4)(2,4):4+16=204 + 16 = 204+16=20Since 20≠−820 \neq -820=−8, point (2,4)(2, 4)(2,4) does not lie on the line.

STEP 5

Test point (−2,−1)(-2, -1)(−2,−1).Substitute x=−2x = -2x=−2 and y=−1y = -1y=−1 into the equation:2(−2)+4(−1)=−82(-2) + 4(-1) = -82(−2)+4(−1)=−8

STEP 6

Calculate the left side of the equation for point (−2,−1)(-2, -1)(−2,−1):−4−4=−8-4 - 4 = -8−4−4=−8Since −8=−8-8 = -8−8=−8, point (−2,−1)(-2, -1)(−2,−1) lies on the line.

STEP 7

Test point (2,1)(2, 1)(2,1).Substitute x=2x = 2x=2 and y=1y = 1y=1 into the equation:2(2)+4(1)=−82(2) + 4(1) = -82(2)+4(1)=−8

STEP 8

Calculate the left side of the equation for point (2,1)(2, 1)(2,1):4+4=84 + 4 = 84+4=8Since 8≠−88 \neq -88=−8, point (2,1)(2, 1)(2,1) does not lie on the line.

STEP 9

Test point (4,4)(4, 4)(4,4).Substitute x=4x = 4x=4 and y=4y = 4y=4 into the equation:2(4)+4(4)=−82(4) + 4(4) = -82(4)+4(4)=−8

STEP 10

Calculate the left side of the equation for point (4,4)(4, 4)(4,4):8+16=248 + 16 = 248+16=24Since 24≠−824 \neq -824=−8, point (4,4)(4, 4)(4,4) does not lie on the line.

STEP 11

Conclusion: The only point that lies on the line 2x+4y=−82x + 4y = -82x+4y=−8 is (−2,−1)(-2, -1)(−2,−1).

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Question6. MJ is creating a graph of the equation $2 x+4 y=-8$ . Which of the following points will lie on the line? a. $(2,4)$ b. $(-2,-1)$ c. $(2,1)$ d. $(4,4)$

Assumptions
1. The equation of the line is given as $2x + 4y = -8$ .
2. We need to determine which of the given points lie on this line.
3. The points to be tested are: a. $(2, 4)$ b. $(-2, -1)$ c. $(2, 1)$ d. $(4, 4)$

To determine if a point lies on the line, substitute the $x$ and $y$ values of the point into the equation $2x + 4y = -8$ . If the equation holds true, then the point lies on the line.

Test point $(2, 4)$ .
Substitute $x = 2$ and $y = 4$ into the equation:
$2(2) + 4(4) = -8$

Calculate the left side of the equation for point $(2, 4)$ :
$4 + 16 = 20$
Since $20 \neq -8$ , point $(2, 4)$ does not lie on the line.

Test point $(-2, -1)$ .
Substitute $x = -2$ and $y = -1$ into the equation:
$2(-2) + 4(-1) = -8$

Calculate the left side of the equation for point $(-2, -1)$ :
$-4 - 4 = -8$
Since $-8 = -8$ , point $(-2, -1)$ lies on the line.

Test point $(2, 1)$ .
Substitute $x = 2$ and $y = 1$ into the equation:
$2(2) + 4(1) = -8$

Calculate the left side of the equation for point $(2, 1)$ :
$4 + 4 = 8$
Since $8 \neq -8$ , point $(2, 1)$ does not lie on the line.

Test point $(4, 4)$ .
Substitute $x = 4$ and $y = 4$ into the equation:
$2(4) + 4(4) = -8$

Calculate the left side of the equation for point $(4, 4)$ :
$8 + 16 = 24$
Since $24 \neq -8$ , point $(4, 4)$ does not lie on the line.

Conclusion: The only point that lies on the line $2x + 4y = -8$ is $(-2, -1)$ .