The function f(x) is to be graphed on a coordinate plane.

What's the slope-intercept form that passes through the points (0, -1) and (1, 5)?

Rzqust [24]

Answer:

Step-by-step explanation:

$\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}$

(0, -1) ⇒ x₁ = 0, y₁ = -1

(1, 5) ⇒ x₂ = 1, y₂ = 5

So the slope:

$\bold{m=\dfrac{5+1}{1-0}=\dfrac{6}{1}=6}$

The slope-intercept form of the equation of line is y = mx + b, where m is the slope and b is the y-intercept of the line.

(0, -1) ⇒ x₀ = 0, y₀ = -1 ⇒ b = -1

Therefore:

y = 6x - 1 ← the slope-intercept form of the equation

5 0

3 years ago

*20 POINTS*

Paraphin [41]

Answer:

If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.

P: ±1, ±2, ±3, ±6 (all prime factors of constant term)

Q: ±1, ±7 (all prime factors of the leading coefficient)

P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7 (all possible values of P/Q)

Now, start testing your values of P/Q in your polynomial:

f(x)=7x4-9x3-41x2+13x+6

You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):

f(2)=7(16)-9(8)-41(4)+13(2)+6

112-72-164+26+6 ≠ 0

f(-2)=7(16)-9(-8)-41(4)+13(-2)+6

112+72-164-26+6 = 0 OK!! There is a zero at x=-2

This means (x+2) is a factor of the polynomial.

Now, do synthetic division to find the polynomial that results from

(7x4-9x3-41x2+13x+6)÷(x+2):

-2⊥ 7 -9 -41 13 6

-14 46 -10 -6

7 -23 5 3 0 The remainder is 0, as expected

The quotient is a polynomial of degree 3:

7x3-23x2+5x+3

Now, continue testing the P/Q values with this new polynomial. Try f(3):

f(3)=7(27)-23(9)+5(3)+3

189-207+15+3 = 0 OK!! we found another zero at x=3

Now, another synthetic division:

3⊥ 7 -23 5 3

21 -6 -3_

7 -2 -1 0

The quotient is a quadratic polynomial:

7x2-2x-1 This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:

x= (1±2√2)÷7

The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7

Step-by-step explanation:

7 0

3 years ago

Vladimir is walking down the street at a speed of 4 miles per hour. Write an equation for the distance in miles, d, that Vladimi

zubka84 [21]

Answer:

$d=4t$

Step-by-step explanation:

We have been given that Vladimir is walking down the street at a speed of 4 miles per hour. We are asked to write an for the distance in miles, d, that Vladimir walks over time in hours, t.

We will use rate formula to solve our given problem.

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Distance}=\text{Speed}\times\text{Time}$

Upon substituting our given information in distance equation, we will get:

$d=4\cdot t$

$d=4t$

Therefore, the equation $d=4t$ represents the distance that Vladimir walks over time in hours.

8 0

4 years ago

Stacey and Michele both babysit in the evening.staceys hours rate is $10 for one child plus $2per additional child Michael hourl

lara31 [8.8K]

They have two children...
8 + 3c = 10 + 2c
c = 2

7 0

3 years ago

Read 2 more answers

Which graph represents the given inequality y>5x-2 I don't have the graphs but I really need an answer to this it must be rig

GarryVolchara [31]

Check attached image file.

4 0

3 years ago

Read 2 more answers