What is the equation of the line through (2, -4) and (0, 4)?

1 answer:

4 0

Answer: C

m = slope

m = (y2 - y1) / (x2 - x1)

2 points:
(2, -4) x1 = 2 and y1 = -4
(0, 4) x2 = 0 and y2 = 4

m = (4 - (-4)) / (0- 2)

m = 8 / -2

m = -4

Equation of the line is : y = mx + b

So we got...

y = -4x + b

Then we can use any of the two points given to solve for b. I’m going to use (0, 4).

y = -4x + b

4 = -4(0) + b

4 = 0 + b

4 = b

Therefore the equation of the line is
y = -4x + 4

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Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1

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Answer:

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Step-by-step explanation:

Hi there!

Background of the Discriminant

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When $b^2-4ac$ is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

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$3x^2+5x=-1$

We're given the above equation. It hasn't been organised completely in $ax^2+bx+c=0$ , but we can change that by adding 1 to both sides to make the right side equal to 0:

$3x^2+5x+1=0$

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

$D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13$

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I hope this helps!

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Cramer's rule works as follows:
x+3y=16
3x+y=8
Then
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y=Dy/D
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Check:
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