You have learned that the \( y \)-intercept of a line is the location where the graph of a line crosses the \( y \)-axis. This location is expressed as an ordered pair, \( (0,\ y) \). The \( x \)-coordinate of the ordered pair that represents a line's \( y \)-intercept is always \( 0 \).
You can read the value of a line's \( y \)-intercept from its graph, from an equation written in slope-intercept form, or from a table of values. For example:
The graph, equation, and table of values shown all represent the same line. What are the coordinates of the line's \( y \)-intercept?
Graph of \( y = - x + 2 \)
\( y = - 1x + 2 \)
\( x \)
\( y \)
\( - 6 \)
\( 8 \)
\( - 1 \)
\( 3 \)
\( 0 \)
\( 2 \)
\( 1 \)
\( 1 \)
\( 6 \)
\( - 4 \)
You can use any method—the graph, equation, or table of values—to name the \( y \)-intercept of this line.
Using the graph:
Read the graph. The equation crosses the y-axis at \( (0,\ 2) \). This is the value of the \( y \)-intercept.
Using the slope-intercept equation:
A slope-intercept equation has the form \( y = mx + b \) where \( b \) is the value of the \( y \)-intercept.
Read the equation. The value of \( b = 2 \), so the \( y \)-intercept is \( (0,\ 2) \).
Using the table of values:
In a table of values, the columns labeled \( x \) and \( y \) correspond to the ordered pair notation \( (x,\ y) \).
The \( x \)-coordinate of the ordered pair that represents a line's \( y \)-intercept is always \( 0 \). Find this value in the table. It is \( (0,\ 2) \).
Let's Practice
Complete the activity below to practice using graphs, equations, and tables of values to find the \( y \)-intercept of a line. Look at the graph, equation, or table of values on each slide and name the location of the \( y \)-intercept. Be sure to check your answer.
What are the coordinates of this line's \( y \)-intercept?
\( x \)
\( y \)
\( - 16 \)
\( 1 \)
\( - 12 \)
\( 0 \)
\( - 4 \)
\( - 2 \)
\( 0 \)
\( - 3 \)
\( 4 \)
\( - 4 \)
\( (0, - 3) \)
The \( x \)-coordinate of the ordered pair that represents a line's \( y \)-intercept is always \( 0 \). Find this value in the table. It is \( (0, - 3) \).
What are the coordinates of this line's \( y \)-intercept?
Graph of \( y = 5x + 4 \)
\( (0,\ 4) \)
Read the graph. The equation crosses the \( y \)-axis at \( (0,\ 4) \).
What are the coordinates of this line's \( y \)-intercept?
\( y = - \frac{3}{5}x + 5 \)
\( \left( 0,\ 5 \right) \)
A slope-intercept equation has the form \( y = mx + b \). Read the equation. The value of \( b = 5 \), so the \( y \)-intercept is \( (0,\ 5) \).
What are the coordinates of this line's \( y \)-intercept?
\( x \)
\( y \)
\( - 4 \)
\( - 8 \)
\( - 2 \)
\( 5 \)
\( 0 \)
\( - 2 \)
\( 2 \)
\( 1 \)
\( 4 \)
\( 4 \)
\( (0, - 2) \)
The \( x \)-coordinate of the ordered pair that represents a line's \( y \)-intercept is always \( 0 \). Find this value in the table. It is \( (0, - 2) \).
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