The reason you chose the form y=mx+b is because that is the equation of any straight line, also known as a linear equation.
For the 1st hour the cost is $50 whatever is the duration (providing it's 1 hour max.
From one hour and onward the cost becomes an additional $25 per quater of an hour.
If y is the cost and x the number of hours, then the equation becomes :
y =50 + 0.25.x or y =1/4x + 50
In this item, we are given with the slope, m = 2/3 and intercept of (1,1). The equation of the line that contains these properties is,
y - y₁ = m(x - x₁)
Substituting the known values,
y - 1 = (2/3)(x - 1)
Simplifying,
3y - 3 = 2x - 2
Further simplifying,
<em> 2x - 3y = -1</em>
3rd - 25 is the 3rd term in the sequence
