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All courses Algebra I · F-IF.4 22 of 76
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
Use the graph to state the \(y\)-intercept in function notation.
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

Locate the y-intercept

\[\text{marked}~\text{point}:~(0,50)\]

The inspected graph marks (0,50) on the vertical axis; its horizontal coordinate 0 makes it the y-intercept.

02

Decode input and output

\[\text{input}~0~\text{months};~\text{output}~50~\text{dollars}~\text{of}~\text{balance}\]

The graph labels the horizontal axis months and the vertical axis balance in dollars, so the coordinates have these contextual units.

03

Translate the point to notation

\[(0,50)~->~B(\text{input})=\text{output}~->~B(0)=50\]

Function notation places the input 0 inside B's parentheses and the matching balance 50 after the equals sign.

04

State the requested intercept

\[B(0)~=~50\]

This exact notation states that at zero months the account balance is 50 dollars, which is the graph's y-intercept.

+

Another way

  1. Start on the vertical axis where the input is zero, read the marked height 50, and insert those coordinates into B(input)=output.

!

Common mistake

Do not reverse the coordinates to B(50)=0 or attach a per-month unit to 50. The intercept is an initial balance, not a rate.

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.

Solution walkthrough video