The equation of line lm is 5x − y = −4. what is the equation of a line perpendicular to line lm in slope-intercept form that contains point (−3, 2)?

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5x - y = - 4 into this form

Subtract 5x from both sides

- y = - 5x - 4 ( multiply through by - 1 )

y = 5x + 4 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

= - = - , thus

y = - x + c ← is the partial equation

To fond c substitute (- 3, 2) into the partial equation

2 = + c ⇒ c = 2 - =

y = - x + ← in slope- intercept form

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt