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3 years ago

What is the slope for (2, -1)(3,4)?

Mathematics

1 answer:

pshichka [43]3 years ago

7 0

To find the slope, using the coordinates, you will plug them into the slope formula.

Slope formula: $\frac{y_2-y_1}{x_2-x_1}$

You plug in the 2nd Y-cordinate in y2 and the 1st y-coordinate in y one. Then you do the same thing for the-x coordinates. Plug in the 2nd x-cordinate in x2, and 1st x-cordinate in x1.

You plug in 4 and -1 in the y2 and y1, respectively. Also, you plug in 3 and 2 in x2 and x1 respectively

The equation you're going to get after plugging in is:

$\frac{4-(-1)}{3-2}$

4-(-1) is the same as 4+1, so you add them. The subtract 3-2. Then you will end up with the fraction, further solving it will get you your answer.

$\frac{4+1}{3-2}=\frac{5}{1}=5$

The answer you will get is 5 after completing all of the steps with the slope formula.

The slope of the line is 5

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Solve the following systems of equations by substitution method.

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Answer:

1) x = 3 and y = -2

2) x = 2 and y = 1

3) x = -2 and y = -1

4) x = 3 and y = 2

5) x = 2

6) x = 2 and y = -3

7) x = 4 and y = 3

8) x = -3 and y = -6

Step-by-step explanation:

1. Answer :

y = -2

4x - 3y = 18 ----(1)

Substitute y = -2 in (1).

4x - 3(-2) = 18

4x + 6 = 18

Subtract 6 from both sides.

4x = 12

Divide both sides by 4.

x = 3

So,

x = 3 and y = -2

2. Answer :

y = 6x - 11 ----(1)

2x + 3y = 7 ----(2)

Substitute y = 6x - 11 in (2).

2x + 3(6x - 11) = 7

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides.

20x = 40

Divide both sides by 20.

x = 2

Substitute x = 2 in (1).

y = 6(2) - 11

= 12 - 11

= 1

So,

x = 2 and y = 1

3. Answer :

x = -3y - 5 ----(1)

4x - 5y = -3 ----(2)

Substitute x = -3y + 5 in (2).

4(-3y - 5) - 5y = -3

-12y - 20 - 5y = -3

-17y - 20 = -3

Add 20 to both sides.

17y = -17

Divide both sides by 17.

y = -1

Substitute y = -1 in (1).

x = -3(-1) - 5

= 3 - 5

= -2

So,

x = -2 and y = -1

4. Answer :

x = 5y - 7 ----(1)

-2x - 3y = -12 ----(2)

Substitute x = 5y - 7 in (2).

-2(5y - 7) - 3y = -12

-10y + 14 - 3y = -12

-13y + 14 = -12

Subtract 14 from both sides.

-13y = -26

Divide both sides by -13.

y = 2

Substitute y = 2 in (1).

x = 5(2) - 7

= 10 - 7

= 3

So,

x = 3 and y = 2

5. Answer :

5x + 3y - 8 = 0 ----(1)

2x - 3y - 6 = 0 ----(2)

Solve for 3y in (1).

5x + 3y - 8 = 0

Subtract 5x from both sides.

3y - 8 = -5x

Add 8 to both sides.

3y = -5x + 8

Substitute 3y = -5x + 8 in (2).

2x - (-5x + 8) - 6 = 0

2x + 5x - 8 - 6 = 0

7x - 14 = 0

Add 14 to both sides.

7x = 14

Divide both sides by 7.

x = 2

6. Answer :

x - 3y - 11 = 0 ----(1)

5x + y - 7 = 0 ----(2)

Solve for x in (1).

x - 3y - 11 = 0

Subtract 3y and 11 to both sides.

x = 3y + 11 ----(3)

Substitute x = 3y + 11 in (2).

5(3y + 11) + y - 7 = 0

15y + 55 + y - 7 = 0

16y + 48 = 0

Subtract 48 from both sides.

16y = -48

Divide both sides by 16.

y = -3

Substitute y = -3 in (3).

x = 3(-3) + 11

= -9 + 11

= 2

So,

x = 2 and y = -3

7. Answer :

2x - 3y = -1 ----(1)

y = x - 1 ----(2)

Substitute y = x - 1 in (1).

2x - 3(x - 1) = -1

2x - 3x + 3 = -1

-x + 3 = -1

Subtract 3 from both sides.

-x = -4

Multiply both sides by -1.

x = 4

Substitute x = x in (3).

y = 4 - 1

= 3

So,

x = 4 and y = 3

8. Answer :

-4x + y = 6 ----(1)

-5x - y = 21 ----(2)

Solve for y in (1).

-4x + y = 6

Add 4x to both sides.

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

Substitute y = 4x + 6 in (2).

-5x - (4x + 6) = 21

-5x - 4x - 6 = 21

-9x - 6 = 21

Add 6 to both sides.

-9x = 27

Divide both sides by -9.

x = -3

Substitute x = -3 in (3).

y = 4(-3) + 6

= -12 + 6

= -6

So,

x = -3 and y = -6

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Answered by: ms115

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