Standard Form of an Equation - WORD PROBLEMS - Free Printable

Let’s solve this step by step.

We are told:
- Jack spent $10 total on games and rides.
- Games cost $1 each → let x = number of games
- Rides cost $2 each → let y = number of rides

So, the equation is:
x + 2y = 10

This is already in standard form (Ax + By = C), so we don’t need to rewrite it.

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Step 1: Find the x-intercept

The x-intercept is where y = 0 (no rides, only games).

Plug y = 0 into the equation:

x + 2(0) = 10
→ x + 0 = 10
→ x = 10

So, the x-intercept is (10, 0)

Interpretation: If Jack goes on 0 rides, he can play 10 games with his $10.

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Step 2: Find the y-intercept

The y-intercept is where x = 0 (no games, only rides).

Plug x = 0 into the equation:

0 + 2y = 10
→ 2y = 10
→ y = 5

So, the y-intercept is (0, 5)

Interpretation: If Jack plays 0 games, he can go on 5 rides with his $10.

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Now, you’re asked to graph this. You would plot the two points:
- (10, 0) — on the x-axis
- (0, 5) — on the y-axis

Then draw a straight line connecting them. Since you can’t have negative games or rides, you’d only consider the part of the line in the first quadrant (where x ≥ 0 and y ≥ 0).

Also, since you can only buy whole numbers of games and rides, the actual solutions are the points on that line where both x and y are whole numbers (like (0,5), (2,4), (4,3), (6,2), (8,1), (10,0)).

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Final Answer:

x-intercept: (10, 0)
Interpretation: Jack can play 10 games if he goes on 0 rides.

y-intercept: (0, 5)
Interpretation: Jack can go on 5 rides if he plays 0 games.