1. your distance from lightning varies directly with the time it takes you to hear thunder
you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the
lightning
a. write a direct variation equation for the relationship between time and distance

d = 1/5t

Step-by-step explanation:

Since it is a direct variation , Let d represent the distance and t represent the time ,then

d ∝ t

introducing the proportionality constant, we have

d = kt

Substituting t = 10 and d = 2 , we have

2 = 10k

k = 1/5

substitute k = 1/5 into the original equation , we have

d = 1/5t

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form