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White raven [17]
3 years ago
5

What is the slope of the line that passes through (3,-4) and (-2,6)

Mathematics
1 answer:
Phoenix [80]3 years ago
5 0

Answer:

slope = -2

Step-by-step explanation:

Slope formula: \frac{y2-y1}{x2-x1}

Given points:

(3 -4) = (x1, y1)

(-2, 6) = (x2, y2)

To find the slope, input the given points into the slope formula:

\frac{6-(-4)}{-2-3}

Solve:

6 - (-4) = 6 + 4 = 10

-2 -3 = -5

Simplify:

\frac{10}{-5}=\frac{2}{-1}=-2

The slope is -2.

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andreyandreev [35.5K]

Answer:

The given system of equations has solutions below:

1) The solution is (2,3)

2) The solution is (\frac{-8}{7}, \frac{5}{7})

3) The solution is infinitely many solutions

4) No solution

Step-by-step explanation:

Given system of equation are

-x+2y=4\hfill (1)

-4x+y=-5\hfill (2)

To solve equation by using elimination method

Multiply eqn (2) into 2

-8x+2y=-10\hfill (3)

Now subtracting (1) and (3)

-x+2y=4

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x=\frac{14}{7}

x=2

Substitute x=2 in equation (1)

-2+2y=4

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y=\frac{6}{2}

y=3

Therefore the solution is (2,3)

2) Given equation is

-2x+y=3\hfill (1)

4y-4=x

Rewritting as below

x-4y=-4\hfill (2)

To solve equation by using elimination method

multiply (2) into 2

2x-8y=-8\hfill (3)

Adding (1) and (3)

-2x+y=3

2x-8y=-8

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y=\frac{5}{7}

substitute y=\frac{5}{7} in (1)

-2x+\frac{5}{7}=3

-2x=3-\frac{5}{7}

-2x=\frac{21-5}{7}

x=-\frac{8}{7}

Therefore the solution is (\frac{-8}{7},\frac{5}{7})

3) Given equation is 6x+2y=10\hfill (1)

3x+y=5\hfill (2)

equation (1) can be written as

2(3x+y)=10

3x+y=\frac{10}{2}

3x+y=5

Therefore equations (1) and (2) are same therefore it has infinitely many solutions

4) Given equation is -x-2y=14\hfill (1)

-2x-4y=12\hfill (2)

multiply equation (1) into 2

-2x-4y=28\hfill (3)

To solve equation by using elimination method

subtracting (2) and (3)

-2x-4y=28

-2x-4y=12

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28\neq -12

therefore it has no solution

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