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muminat
3 years ago
10

Which graph represents the function y = 2x – 4? A coordinate plane with a line passing through (negative 4, 0) and (0, 2). A coo

rdinate plane with a line passing through (0, negative 4) and (4, negative 2). A coordinate plane with a line passing through (0, negative 4) and (2, 0). A coordinate plane with a line passing through (negative 4, 0) and (negative 2, 4).
Mathematics
2 answers:
VARVARA [1.3K]3 years ago
8 0

Answer:

The third option: "A coordinate plane with a line passing through (0, negative 4) and (2, 0)."

Step-by-step explanation:

Use the equation defined by the function: y = 2x - 4 to check the (x, y) values they give you. If they both render true mathematical statements, those are indeed points on the plane that belong to the given line.

For the third case; the pairs (0,-4) and (2,0), both satisfy the equation of the line that is given.

For (0,-4):  y = 2x - 4 becomes:

(-4)=2(0)-4\\-4=0-4\\-4=-4 which is a TRUE statement

For (2,0):  y = 2x - 4 becomes:

(0)=2(2)-4\\0=4-4\\0=0 which is also a TRUE statement.

This option is the only one that verifies both given points as truly being part of the given line.

nata0808 [166]3 years ago
3 0

Answer:  The correct option is

(C) A coordinate plane with a line passing through (0, negative 4) and (2, 0).

Step-by-step explanation:  We are given to select the option that represents the following function :

y=2x-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Now, we know that the equation of a line passing through two points (a, b) and (c, d) is given by

y-b=\dfrac{d-b}{c-a}(x-a).

<em><u>Option (A) :</u></em> The line passing through the points (-4, 0) and (0, 2) is

y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\\\\\\Rightarrow y=\dfrac{1}{2}(x+4)\\\\\\\Rightarrow y=\dfrac{1}{2}x+2, not same as equation (i).

So, option (A) is NOT correct.

<em><u>Option (B) :</u></em> The line passing through the points (0, -4) and (4, -2) is

y-(-4)=\dfrac{-2-(-4)}{4-0}(x-0)\\\\\\\Rightarrow y+4=\dfrac{1}{2}x\\\\\\\Rightarrow y=\dfrac{1}{2}x-4, not same as equation (i).

So, option (B) is NOT correct.

<em><u>Option (C) :</u></em> The line passing through the points (0, -4) and (2, 0) is

y-(-4)=\dfrac{0-(-4)}{2-0}(x-0)\\\\\\\Rightarrow y+4=2x\\\\\\\Rightarrow y=2x-4, which is same as equation (i).

So, option (C) is CORRECT.

<em><u>Option (D) :</u></em> The line passing through the points (-4, 0) and (-2, 4) is

y-0=\dfrac{4-0}{-2-(-4)}(x-(-4))\\\\\\\Rightarrow y=2(x-(-4))\\\\\\\Rightarrow y=2x+8, not same as equation (i).

So, option (D) is COT correct.

Thus, the correct option is (C).

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Answer:

(A) y+4=-3(x+6)

Step-by-step explanation:

The point-slope form of the equation of a line whose slope is m and passes through the point (x_1, y_1) is: y-y_1=m(x-x_1)

Given the point: (x_1, y_1)=(-6,-4)

Slope, m=-3

x_1=-6\\y_1=-4

Substituting these values into:  y-y_1=m(x-x_1), we obtain the point slope form of the equation:

y-(-4)=-3(x-(-6))\\\\y+4=-3(x+6)

The correct option is A.

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What is the solution to the equation ?
Savatey [412]

Answer:

There is no solution of the system of equations.

Step-by-step explanation:

We are given two equations y = - 4 and y = 4 and are to find the solution to the equations.

Now, the straight line y = - 4 is parallel to the x-axis as the equation of straight lines that are parallel to the x-axis are given by y = c, where c is any constant value.

Again, the straight line y = 4 is parallel to the x-axis.

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6 0
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(04.03 MC)
Vlad1618 [11]

Answer:

x = -2 and y = 3

{y = -3 x - 3, y = (3 x)/4 + 9/2} = x = -2 and y = 3

Step-by-step explanation:

Solve the following system:

{6 x + 2 y = -6

3 x - 4 y = -18

Express the system in matrix form:

(6 | 2

3 | -4)(x

y) = (-6

-18)

Solve the system with Cramer's rule:

x = -6 | 2

-18 | -4/6 | 2

3 | -4 and y = 6 | -6

3 | -18/6 | 2

3 | -4

Evaluate the determinant 6 | 2

3 | -4 = -30:

x = -6 | 2

-18 | -4/(-30) and y = 6 | -6

3 | -18/(-30)

Simplify -6 | 2

-18 | -4/(-30):

x = -1/30 -6 | 2

-18 | -4 and y = 6 | -6

3 | -18/(-30)

Simplify 6 | -6

3 | -18/(-30):

x = -(-6 | 2

-18 | -4)/30 and y = -1/30 6 | -6

3 | -18

Evaluate the determinant -6 | 2

-18 | -4 = 60:

x = (-1)/30×60 and y = -(6 | -6

3 | -18)/30

(-1)/30×60 = -2:

x = -2 and y = -(6 | -6

3 | -18)/30

Evaluate the determinant 6 | -6

3 | -18 = -90:

x = -2 and y = (-1)/30×-90

(-1)/30 (-90) = 3:

Answer: x = -2 and y = 3

___________________________________________

Solve the following system:

{y = -3 x - 3

y = (3 x)/4 + 9/2

Express the system in standard form:

{3 x + y = -3

-(3 x)/4 + y = 9/2

Express the system in matrix form:

(3 | 1

-3/4 | 1)(x

y) = (-3

9/2)

Write the system in augmented matrix form and use Gaussian elimination:

(3 | 1 | -3

-3/4 | 1 | 9/2)

Add 1/4 × (row 1) to row 2:

(3 | 1 | -3

0 | 5/4 | 15/4)

Multiply row 2 by 4/5:

(3 | 1 | -3

0 | 1 | 3)

Subtract row 2 from row 1:

(3 | 0 | -6

0 | 1 | 3)

Divide row 1 by 3:

(1 | 0 | -2

0 | 1 | 3)

Collect results:

Answer:  {x = -2 , y = 3

5 0
2 years ago
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