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2 years ago

Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.

Mathematics

2 answers:

erica [24]2 years ago

8 0

Answer:

y = 2x + 4.

Step-by-step explanation:

The slope = the slope of y = 2x - 3 which is 2.

Using the point-slope form:

y - y1 = 2(x - x1)

Using the point (-1, 2):

y - 2 = 2(x - -1)

y = 2x + 2 + 2

y = 2x + 4 is the answer.

sammy [17]2 years ago

7 0

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be $m = 2.$

$y = 2x + b$

We substitute the given point to find b:

$2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4$

Finally the line is:

$y = 2x + 4$

Answer:

$y = 2x + 4$

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Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

Step-by-step explanation:

<u>Increasing and Decreasing Intervals of Functions</u>

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

3 0

2 years ago

I don’t know what to do with the 3 feet above the ground

Slav-nsk [51]

Answer:

3 seconds

Step-by-step explanation:

You want to set h(t)=3, then take the root such that t≠0. You would have:

3=3+48t−16t^2

Let's solve your equation step-by-step.

3=3+48t−16t2

Step 1: Simplify both sides of the equation.

3=−16t2+48t+3

Step 2: Subtract -16t^2+48t+3 from both sides.

3−(−16t2+48t+3)=−16t2+48t+3−(−16t2+48t+3)

16t2−48t=0

Step 3: Factor left side of equation.

16t(t−3)=0

Step 4: Set factors equal to 0.

16t=0 or t−3=0

t=0 or t=3

3 makes more sense than 0 because the ball can't have been in the air for 0 seconds.

So the ball was in the air for 3 seconds.

7 0

2 years ago

The length of a rectangle is eight more than twice its width. The perimeter is 96 feet. Find the dimensions of the rectangle

blagie [28]

Step-by-step explanation:

Length = L

Width = W

L=8 more than 2W

L = 8 * 2W

L = 16W

Perimeter = 96

perimeter is the lengths of all sides added together

2L + 2W = 96

we have

L = 16W

2L + 2W = 96

let's do substitution

put what L = into 2L + 2W = 96

2(16W) + 2W = 96

can you rearrange that to get w

put answer in comment

4 0

1 year ago

Find the slope of the line containing points (1,3) (-3,-8)

Dmitry_Shevchenko [17]

Y=mx+c
1/-3=m3/8+c
m= 11/4

4 0

2 years ago

What is the constant of proportionality for the question (-4x + 8y = 0)?

zubka84 [21]

Answer: 1/2

Step-by-step explanation:

1) Put the equation into y=kx form

- add 4x to both sides

- divide by 8 on both sides to get y=1/2x

2) k is the constant of proportionality

8 0

2 years ago