Alex has been offered $50 to accept the job, plus, $13 per hour. Alex claims he will complete the job in 7 hours. How would you write this as a linear equation in the form of:

c = mt + b

if c is the cost and t is the time, m is the slope, and b is the y-intercept.

Please help!!

y=mx+b

slope is the rate of change and whenever something says per it is a rate. Meaning m=13 and then he already will gain $50 just for accepting. Y-intercept is the initial value, so b=50. t or x is the hours worked=7.
c=30(t)+50 (for any # of hours)
c=30(7)+50 c=260

Well, let's consider each piece we're given:

$50 as a down payment for accepting the job -> This value doesn't change regardless of how many Alex would work on the job. He would get the money ahead of time, meaning that the value is constant and would fit perfectly as our y-intercept.

$13 per hour -> the "per hour" should stand out to you because the amount of money he gets is directly dependent upon how many hours he puts into the job. Say, he worked two hours, he'd make $(13 x 2) for that day. The "per hour" lets us know that we need a variable in place of that for our linear equation ($13 itself doesn't change however, it only changes when it's been affected by some other value, time.)

To write the linear equation in the form c = mt + b, we need to find the values of m, t, and b.

In this case, c represents the cost and t represents the time.

The fixed cost, or the cost that Alex would receive regardless of the time taken, is $50. This can be represented by the y-intercept (b).

The variable cost, or the cost that depends on the time taken, is $13 per hour. This can be represented by the slope (m).

Since Alex claims to complete the job in 7 hours, we can substitute this value for t.

Therefore, the equation can be written as:

c = 13t + 50

By substituting the values of m, t, and b, you can see that the linear equation in the form c = mt + b is c = 13(7) + 50.

Simplifying, we have:

c = 91 + 50
c = 141

So, the cost (c) for completing the job in 7 hours would be $141.