Write an equation of the direct variation that includes the point (–10,

A liner function of x is graphed on a coordinate grid. the points 6,34 and 18,26 lie on the graph of the function what are the r

Lynna [10]

Answer:

Rate of change: m = -2/3

Value of the function at x = 24: y = 22

Step-by-step explanation:

You can write linear functions in <u>slope-intercept form</u>: y = mx + b

"x" and "y" are points on the line

"m" is the slope, how steep the line is, also known as <u>rate of change</u>

"b" is the y-intercept, when the graph hits the y-axis

Find the rate of change of the function by finding the slope between the two given points.

The formula for slope: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Label point 1 and point 2. Label each coordinate; remembered ordered pairs are (x, y).

Point 1 (6, 34) x₁= 6 y₁ = 34

Point 2 (18, 26) x₂ = 18 y₂ = 26

Substitute the points into your equation using the bolded information.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{26-34}{18-6}$ Subtract

$=\frac{-8}{12}$ Reduce the fraction. Top and bottom divide by 4

$=\frac{-2}3}$ Slope of the line, "m"

Substitute the slope and any point you want into slope-intercept form. I choose point (6, 34). x = 6 y = 34 m = -2/3

y = mx + b

34 = (-2/3)(6) + b Multiply to simplify

34 = (-12/3) + b

Start isolating "b"

34 + 12/3 = (-12/3) + 12/3 + b Add 12/3 on both sides

34 + 12/3 = b

Add fractions by combining the whole number into the numerator. Multiply the whole number by the denominator and add to the numerator.

b = (34*3 + 12) / 3 Solve numerator

b = 114/3 Value of "b"

Substitute the values "m" and "b" into slope-intercept form.

y = -2/3 x + 114/3 Equation of the line

To find the x = 24, take the equation of the line and substitute "x" for 24. Then solve for "y".

y = -2/3 x + 114/3 Equation of the line

y = (-2/3)(24) + 114/3

y = (-2*24)/3 + 114/3 Multiply into the numerator

y = (-48)/3 + 114/3 Combine under the same denominator

y = (-48 + 114) / 3 Add

y = 66/3 Divide

y = 22 Value of function

Therefore the rate of change, or slope "m", is -2/3. When "x" is 24, the value of the entire function is 22.

4 0

3 years ago

An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a

sp2606 [1]

Answer:

The probability of selecting an odd number given that the chip is black is 0.454.

Step-by-step explanation:

First of all, the value of probability is always less than 1, so the following value of probabilities need to be corrected and are:

Probability of selecting a black chip with an odd number(A)=0.415

Probability of selecting a black chip(B)= 0.915

Probability of A given B is denoted by=P(A | B)

P(A|B) =P(A∩B)/P(B)

P(B)=0.915

P(A∩B)=0.415

P(A|B)= $\frac{0.415}{0.915}$

P(A|B)=0.454

The probability of selecting an odd number given that the chip is black is 0.454.

7 0

3 years ago

A 13 foot ladder is placed 5 feet away from my wall .The distance from the ground straight up to the top of the wall is 13 foot

zysi [14]

Answer:

no

Step-by-step explanation:

Assuming the wall makes a 90-degree angle with the ground, the ladder is the hypotenuse of a right triangle whose legs are the ground distance, the wall height, and whose hypotenuse is the ladder length.

The hypotenuse of a right triangle must be longer than either side. If one side is length 13 and one side is length 5, the hypotenuse must be about 13.93. A 13-ft ladder will not do.

3 0

3 years ago

4. The circle graph shows how the annual bodget for

Zinaida [17]

Answers:
Set construction:$40,000
Costumes and props:$40,000
Staff salaries:$50,000
Advertising:$30,000
Physical plant:$20,000
Misc:20,000

Explanation:
To get the answers multiply the percentage by the total. You can change the percentage to a decimal by living it two places to the right
Ex:20%=.2—>.2x200,000=40,000

3 0

3 years ago

Richard Hoskins was the leader of a 4-H club with 27 children. When he divided the club into groups of 5 to play a game, how man

kotykmax [81]

Answer:

5 groups

2 extra children

Step-by-step explanation:

The computation of a number of groups and number of extra children is shown below:

Given that

There is 27 children

And, this group would be divided into group 5

So,

As we know that 25 is easily divided by 5

So there are 5 groups

And, the extra children is

= 27 - 25

= 2 chidren

4 0

3 years ago

Write an equation of the direct variation that includes the point (–10, –17).