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coldgirl [10]
2 years ago
10

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

Mathematics
1 answer:
Nonamiya [84]2 years ago
4 0

Answer: y = -1.5x - 3

Step-by-step explanation:

We'll assume this is a straight line, with the form y=mx+b. m is the slope (the rate that y changes with a change in x) and b is the y-intercept (the value of y when x=0).

Once we can determine both m and b, we'll have an equation that answers this question. First, m.

m, the slope, is known as the Rise/Run. We can use the two given points to calculate this value. Take the two points, (-4,3) and (2,-6), and calculate the change in x (the Run), by subtrating the initial point (I'll choose (-4,3)) from the final point ((2,-6)). For x that is: 2-(-4) = 6. For y: -6-3 = -9. When x moved +6 units, y went down by 9, or -9. The slope is the Rise (-9) over the Run (6), or (-9/6). The slope of this line is - 1.5.

We now have y = -1.5x + b. To find b, use wither of the two points. I'll use (2,-6) because I like even numbers, but fell free to use the other. Both will give the same answer for b. [Try it].

Using (2,-6), we get:

y = -1.5x + b

-6 = -1.5*(2) + b

-6 = -3 + b

b = -3

The equation is y = -1.5x - 3

=====

For fun, try the other point, (-4,3) to find the value of b:

y = -1.5x + b

3 = -1.5*(-4) + b

3 = 6 + b

b = -3 The Same!

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2x^2=9-3x <br> Find the factors
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Answer:

x = -3, $ \frac{3}{2} $

Step-by-step explanation:

The given quadratic equation is: $ 2x^2 = 9 - 3x $

This can be written as: $ 2x^2 + 3x - 9 = 0 $

To solve a quadratic equation of the form $ ax^2 + bx + c = 0 $ we use the formula:

           $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Here, a = 2; b = 3; c = - 9

Therefore, the roots of the equation are:

$ x = \frac{- 3 \pm \sqrt{9 - 4(2)(-9)}}{2(2)} $

$ \implies x = \frac{-3 \pm \sqrt{81}}{4} $

$ \implies x = \frac{-3 \pm 9}{4} $

We get two values of 'x', viz.,

x = $ \frac{-3 + 9}{4} $ and $ \frac{- 3 - 9}{4} $

$ \implies x = \frac{6}{4} \hspace{5mm} \& \hspace{5mm} \frac{-12}{4} $

⇒ x = -3, 3/2

Since the factors of the quadratic equation is asked, we write it as:

(x + 3)(x - $ \frac{3}{2} $) = 0

because, if (x - a)(x - b) are the factors of a quadratic equation, then 'a' and 'b' are its roots.

Multiply (x + 3) and (x - $ \frac{3}{2} $ to see that this indeed is the given quadratic equation.

5 0
3 years ago
Matt and Mark went to El Rodeo to have some dinner. Matt ordered 3 tacos and 2 enchiladas, which cost him $4.93. Mark ordered 2
lord [1]

Answer:

The cost of one taco is $0.87 and the cost of one enchilada is $1.16

Step-by-step explanation:

Let the cost of tacos be X

and cost of enchiladas be y

So, by using given data, we have following equations

3X + 2Y = 4.93             (1)

2X + 4Y = 6.38             (2)

So, first multiply 1st equation by 2 and 2nd equation by 3, then subtracting 1st equation by 2nd.

= 2 × ( 3X + 2Y = 4.93)       (1)

= 3 × (2X + 4Y = 6.38)        (2)

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By putting the value of Y in equation 1, we get

3X + 2(1.16) = 4.93

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Hence, the cost of one taco is $0.87 and the cost of one enchilada is $1.16.

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