Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point)

Responses

(y−45)=−5(x−3)
open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren

(y−10)=−5(x+10)
open paren y minus 10 close paren is equal to negative 5 times open paren x plus 10 close paren

(y+10)=−5(x−10)
open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren

(y−3)=−5(x−45)

3 answers

To find the point-slope equation from the two points we have: (3, 45) and (10, 10), we first need to find the slope of the line (m) between these two points.

The formula for the slope (m) between two points (x1,y1) and (x2,y2) is:

m=y2y1x2x1

Using the points (3, 45) (i.e., (x1,y1)=(3,45)) and (10, 10) (i.e., (x2,y2)=(10,10)), we can substitute these values in:

m=1045103=357=5

Now that we have the slope (m = -5), we can use the point-slope form of the equation of a line, which is:

yy1=m(xx1)

Choosing point (3, 45), we substitute into the equation:

y45=5(x3)

So the point-slope equation that corresponds to the given points is:

(y45)=5(x3)

Therefore, the correct response is:

(y−45)=−5(x−3)

Function A: (four points on a graph) (-4, 0) (-2, 1) (0, 2) (2, 3)
Function B: (table chart)
x y
0 3
4 -9
8 -21
Function C: y=x+5
(4 points)
a. Which function has the greatest rate of change (slope)?

b. Which function has the smallest y-intercept?

c. Which function would you want to represent your money earned per hour?

d. Which function would give you the highest initial amount of money?

responses
function A
function B
function C

To analyze the functions provided, let's break each question down step by step:

Function A

Points: (-4, 0), (-2, 1), (0, 2), (2, 3)

To find the slope (rate of change): Using two points, for example, (0, 2) and (2, 3): m=3220=12 You can calculate the slope between any two points to find this was consistent; the slope is 12.

Function B

Table: Misplaced \hline

Finding the slope between the first two points (0, 3) and (4, -9): m=9340=124=3

Finding the slope between the second two points (4, -9) and (8, -21): m=21(9)84=124=3 The slope is consistently 3.

Function C

Equation: y=x+5

The slope (rate of change) is: 1 (the coefficient of x).

Comparing Slopes

  • Function A: slope = 12
  • Function B: slope = 3
  • Function C: slope = 1

Greatest Rate of Change:

  • Function C has the greatest slope of 1.

Finding y-intercepts

  • Function A's y-intercept: When x=0, y=2.
  • Function B's y-intercept: When x=0, y=3.
  • Function C's y-intercept: When x=0, y=5.

Smallest Y-Intercept:

  • Function A: 2
  • Function B: 3
  • Function C: 5

The smallest y-intercept is from Function A.

Money Earned per Hour

Generally, you might prefer a function with a positive slope representing earnings, and you want it to be as high as possible.

  • Function A has a positive slope (12).
  • Function C has a slope of 1.

Function C would represent the best option for money earned per hour since it has a positive slope and does not dip.

Highest Initial Amount of Money

The initial amount of money is represented by the y-intercept.

  • Function A = 2
  • Function B = 3
  • Function C = 5

The highest initial amount of money is from Function C.

Answers

a. Function C (greatest rate of change)
b. Function A (smallest y-intercept)
c. Function C (best for money earned per hour)
d. Function C (highest initial amount of money)

Would you like to clarify further or provide more detail for any of these points?