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What is the equation for the line with a slope of - 2/3 that passes through (0, -2)

viktelen [127]

Answer:

y= -2/3x-2

Step-by-step explanation:

Since we have a point and a slope, we can use the point slope formula

$y-y_{1} =m(x-x_{1})$

m is the slope. In this case, m is -2/3

y1 is the y coordinate of the point. In this case, it is -2

x1 is the x coordinate. In this case it is 0.

We can substitute these values into the formula

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

Distribute -2/3

y+2 = -2/3*x + -2/3*0

y+2= -2/3x+0

Subtract 2 from both sides. We want to get y by itself. This is because we want our line to be in y=mx+b form.

y+2-2= -2/3x+0-2

y= -2/3x -2

5 0

3 years ago

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9

Minchanka [31]

Answer:

$f(x) = x + 4$

Step-by-step explanation:

First create an equation in slope-intercept form, y = mx + b. To do this, find the rate of change or slope (m), and the y-intercept (b).

Using two pairs, (-7, -3) and (-8, -4),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{-8 -(-7)} = \frac{-1}{-1} = 1$

m = 1

To find b, substitute m = 1, x = -7 and y = -3 into y = mx + b.

Thus:

-3 = (1)(-7) + b

-3 = -7 + b

-3 + 7 = b

4 = b

b = 4.

Replace y with f(x), m with 1 and b with 4 in y = mx + b.

The function would be:

$f(x) = x + 4$

6 0

3 years ago

Help please hekfkdnr

mamaluj [8]

Answer:

first one is -16

second is -4

I'm what the third is

5 0

3 years ago

For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts? a) m>12/49 b) m<12/49 c) m<49/12 d) m&g

den301095 [7]

The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":

Δ=b2−4ac Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios: if→Δ>0=>∃x1,x2/ax2+bx+c=0 This just means: "if the discriminant is greater than zero, there will exist two x-intercepts" And for the second scenario: if→Δ=0→∃xo/ax2+bx+c=0 This means: "if the discriminant is equal to zero, there will be one and only one x-intercept" And for the last scenario: if→Δ<0→∃x∉R/ax2+bx+c=0 This means that :"if the discriminant is less than zero, there will be no x-intercepts" So, if we take your excercise and analyze the the discriminant: 3x2+7x+m=y we will find the values that satisfy y=0 : 3x2+7x+m=0 And we'll analyze the discriminant: Δ=72−4(3)(m) And we are only interested in the values that make the discriminant equal zero: 72−4(3)(m)=0 All you have to do is solve for "m".

6 0

3 years ago

How many zeros are in the product of any nonzero whole number less than 10 and 500

worty [1.4K]

Answer:

If the non-zero whole number is even, then there are 3 zeroes

If the non-zero whole number is odd, then there are 2 zeroes

Step-by-step explanation:

* Lets explain the information in the problem

- Whole numbers are positive numbers, including zero, without

any decimal or fractional

- Nonzero whole numbers are positive numbers, not including zero

- The non-zero whole numbers less then 10 are:

1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

- The product of any nonzero whole number less than 10 and 500

means multiply any of nonzero number above by 500

- The number of zeros in the product is equal to the sum of the

number of zeros at the end of each of the factors.

# 1 × 500 = 5 × 100 ⇒ 2 zeros

# 2 × 500 = 2 × 5 × 100 = 10 × 100 ⇒ 3 zeros

# 3 × 500 = 3 × 5 × 100 = 15 × 100 ⇒ 2 zeros

# 4 × 500 = 2 × 2 × 5 × 100 = 2 × 10 × 100 ⇒ 3 zeros

# 5 × 500 = 5 × 5 × 100 = 25 × 100 ⇒ 2 zeroes

# 6 × 500 = 2 × 3 × 5 × 100 = 3 × 10 × 100 ⇒ 3 zeros

# 7 × 500 = 7 × 5 × 100 = 35 × 100 ⇒ 2 zeroes

# 8 × 500 = 2 × 2 × 2 × 5 × 100 = 4 × 10 × 100 ⇒ 3 zeros

# 9 × 500 = 3 × 3 × 5 × 100 = 45 × 100 ⇒ 2 zeros

- From all answers above:

# If the non-zero whole number is even (2 , 4 , 6 , 8), then there are

3 zeros in the product

# If the non-zero whole number is odd (1 , 3 , 5 , 7 , 9), then there are

2 zeros in the product

8 0

3 years ago