Solve the equation

Question

h(x)=5x+2, find h(x+h)-h(x)

Answer 1

For h(x+h) you sub x+h in where there is an x, so 5(x+h)+2

You already know what h(x) is, 5x+2

h(x+h)-h(x) = 5(x+h)+2 - (5x+2) and simplify

= 5x+5h+2-(5x+2)

You should be able to complete the rest.

Answer 2

f(x) = 5x+2

f(x+h) = 5(x+h) + 2 = 5x +5h +2

f(x+h)- f(x) = 5x+5h+2 - (5x+2) = 5x+5h+2 - 5x-2 = 5h

this is typically part of the difference quotient where you find the limit of

[f(x+h)-f(x)]/h as h goes to zero. since you can't divide by zero, you can't just replace h by 0

so you calculate f(x+h)-f(x) and divide the result by h which gives 5h/h = 5

5 is the derivative of f(x) = f'(x)

this is all preparation to learn how to do differential calculus. And finding the slope of a line

y=5x + 2 is in y=mx +b form where m=slope= 5

but this method works for lines that are straight or curved.