What is the equation of the line described below written in slope-intercept form? the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 y = -x + 1 y = x - 1 y = 2x + 1

The equation of the perpendicular line

Step-by-step explanation:

Given: The line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.

The equation of line given in standard form.

We need to write in slope-intercept form.

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

2x - y - 7 = 0

Step 1:

Add 7 on both sides, we get

2x - y - 7 + 7 = 0 + 7   [Addition of equality]

2x - y = 7

Step 2:

Subtract 2x from both sides, we get

2x - 2x - y = -2x + 7

-y = -2x + 7

Step 3:

We have negative y, we need to make it positive, so we need to multiply both sides by -1.

-1(-y) = -1(-2x + 7)

y = 2x - 7

Here slope (m) = 2 and y-intercept (b) = -7

Now we have to find the perpendicular line.

The slope of the perpendicular line is negative reciprocal of the slope of the given line.

So, m = -1/2

Now we have to find y-intercept.

We are given a point (4, -1)

Now plug in x = 4 and y = -1 in y = -1/2x + b

-1 = -1/2(4) + b

-1 = -2 + b

b = -1 +2

b = 1

So, the equation of the perpendicular line

1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).