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All courses Math I · F-IF.4 22 of 59
Interpret and sketch key graph/table features in context: intercepts, intervals, maxima/minima, symmetry, end behavior, and periodicity.

Interpret a y-intercept in context

Problem
Which choice identifies the y-intercept shown on the graph?
Line graph for account balance after x months with a marked point at (0, 50). Open full size
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Hint

Use the point (0,50): identify what x = 0 means and what the y-value 50 measures.

A y-intercept gives the output value when x = 0. In this context, x is months and the output is account balance.

Solution walkthrough

01

Read the point

\[(0,50)\]

The y-intercept is the point where x equals 0.

02

Interpret the input

\[x~=~0~\text{months}\]

In this graph, x measures months, so x = 0 means the starting time before any months have passed.

03

Interpret the output

\[\text{balance}~=~50~\text{dollars}\]

The y-value gives the account balance at that starting time.

04

State the interpretation

\[\text{statement}~=~B(0)=50;~\text{input}~=~0~\text{months}~\text{after}~\text{opening};~\text{output}~=~\$50~\text{balance};~\text{interpretation}~=~\text{the}~\text{account}~\text{opened}~\text{with}~a~\$50~\text{balance}\]

Putting the coordinates into context gives the initial balance.

+

Another way

  1. Read a y-intercept as initial value: when the input is 0 months, the output is the starting account balance.

!

Common mistake

A common mistake is to interpret 50 as a monthly change. The point (0,50) gives the balance at x = 0 months, not the rate of change per month.

Line graph for account balance after x months with the y-intercept point 0 comma 50 marked, showing the account started with 50 dollars.
At 0 months, the account balance is 50 dollars, so the account started with 50 dollars.