Today, john ran 15 miles in 2 hours and 30 minutes. he wants to represent the relationship between the distance he ran, in miles, and the time, in hours, as proportional in order to examine his times at various distances. write an equation that john can use to represent a proportional relationship between distance, d, in miles, and time, t, in hours.

d = 6t

Step-by-step explanation:

Firstly, lets change the 2 hours and 30 minutes to 2.5 hours, you could devide the time in minutes by 60 to get that number 2[hours]+()[minutes to hours] = 2.5Hours.

Anyway, John ran 15 miles in 2.5 hours which means he ran (15÷2.5) in one hour which is equal to 6miles per hour. That means if you multiply the hours he ran by 6 you will get the miles he ran.

So the answer would be:

d = 6t

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