An equipment rental company charges $40 per day to rent a trench digger. A construction crew rented a trench digger for 6 days and paid 270. Write a linear equation in slope-intercept form that represents the total cost to rent the trench digger as a function of the number of days.

Please check the explanation.

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

where m is the slope or rate of change and b is the y-intercept

An equipment rental company charges $40 per day to rent a trench digger.

It means the rate of change = $40 per day

We know that the rate of change is also termed as the slope.

Thus,

m = 40

Given that a construction crew rented a trench digger for 6 days and paid 270.

It means at x = 6, y = 270

substituting (x, y) = (6, 270) and m = 40 in the slope-intercept form to determine the y-intercept 'b'

y = mx+b

270 = 40(6) + b

270 = 240 + b

b = 270 - 240

b = 30

Thus, the y-intercepy b = 30

Now, substituting m = 40 and b = 30 in the slope-intercept form

y = mx + b

y = 40x + 30

Thus, the equation of line in the slope-intercept form is

y = 40x + 30

VERIFICATION:

Put x = 6, in the equation to determine the total cost for 6 days

y = 40x + 30

y = 40(6) + 30

y = 240 + 30

y = $270

Thus, the total cost for days rent = $270

Therefore, x must be equal to 6 i.e. x = 6 to find the total cost i.e. y = 270.