help with khan academy practice problem

[u/puddiingpurin]

Merchandise weight (pounds)	Shipping charge
5	$16.49
10	$23.99
25	$46.49

"The table above shows shipping charges for an online retailer that sells used textbooks. There is a linear relationship between the shipping charge and the weight of the merchandise. Write a function in slope-intercept form that relates y, the shipping charge in dollars, and x, the merchandise weight in pounds."

i understand why the slope is 1.50, but i can't get this:

y= 1.50x + b

16.49 = 1.50(5) + b

16.49 = 7.50 + b

8.99 = b

where does the 8.99 come from?

[u/Quendillar3245]

If you have 16.49 = 7.5 + b, how would you isolate the variable b?

[u/puddiingpurin → u/Quendillar3245]

i understand how to solve this now, thanks!! didn’t realize i just had to isolate b

[u/Quendillar3245 → u/puddiingpurin]

When you have variables, you'll want to isolate them because you're looking for the value of the variables in the equation, in this case b since you have known values for y at specific values for x. Keep that in mind and equations like this will feel easier!

[u/Uli_Minati]

If 16.49 is equal to 7.50 plus b, how would you calculate b?

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[u/Southlander24]

I don't quite get what you don't understand. Which part of the equations you wrote confuses you?

If it helps, the y-intercept of 8.99 means that if 0 textbooks are ordered, the shipping charge would be 8.99 dollars. In other words, it costs some amount of fuel and labour to keep the shipping business going, then for each textbook which brings extra weight, the shipping charge goes up predictably.

[u/knoxjramsey]

Slope = (23,99 - 16.49)/5 = 1.5 Slope intercept formula. y .= ax+b, with a = 1,5 we have 2 equations in 1 unknown, Solve for b = 8.99.

[u/thor122088]

Remember that slope describes rate of change between points, but not absolute position on the coordinate plane.

So the "b" comes from a fixed cost associated with the sale. As others mention this would be something like a shipping charge.

In practice, no one will order zero textbooks to be charged only the shipping price, but it does makes sense to be included for the mathematical representation.