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### Course: 8th grade (Illustrative Mathematics)>Unit 3

Lesson 11: Extra practice: Intercepts

# Intercepts of lines review (x-intercepts and y-intercepts)

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

## What are intercepts?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
A coordinate plane. The x- and y-axes each scale by one. The graph of the line is labeled y equals one-half x minus three. The y-intercept is labeled at the point zero, negative three. The x-intercept is labeled the point six, zero.
Want a deeper introduction to intercepts? Check out this video.

## Example: Intercepts from a graph

Looking at the graph, we can find the intercepts.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, four and five, zero.
The line crosses the axes at two points:
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, four and five, zero. Both of these points are plotted.
The point on the x-axis is left parenthesis, 5, comma, 0, right parenthesis. We call this the x-intercept.
The point on the y-axis is left parenthesis, 0, comma, 4, right parenthesis. We call this the y-intercept.

## Example: Intercepts from a table

We're given a table of values and told that the relationship between x and y is linear.
xy
1minus, 9
3minus, 6
5minus, 3
Then we're asked to find the intercepts of the corresponding graph.
The key is realizing that the x-intercept is the point where y, equals, 0, and the y-intercept is where x, equals, 0.
A table of values. The left column is labeled x, and the right column is labeled y. When x is negative one, y is negative twelve. When x is one, y is negative nine. When x is three, y is negative six. When x is five, y is negative three. When x is seven, y is zero. Between every x-value there is a plus two which highlights the change of the x-values. Between every y-value there is a plus three which highlights the change of the y-values.
The point left parenthesis, 7, comma, 0, right parenthesis is our x-intercept because when y, equals, 0, we're on the x-axis.
To find the y-intercept, we need to "zoom in" on the table to find where x, equals, 0.
A table of values. The left column is labeled x, and the right column is labeled y. When x is negative one, y is negative twelve. When x is zero, y is negative ten point five. When x is one, y is negative nine. Between every x-value there is a plus one which highlights the change of the x-values. Between every y-value there is a plus one point five which highlights the change of the y-values.
The point left parenthesis, 0, comma, minus, 10, point, 5, right parenthesis is our y-intercept.

## Example: Intercepts from an equation

We're asked to determine the intercepts of the graph described by the following linear equation:
3, x, plus, 2, y, equals, 5
To find the y-intercept, let's substitute start color #6495ed, x, end color #6495ed, equals, start color #6495ed, 0, end color #6495ed into the equation and solve for y:
\begin{aligned}3\cdot\blue{0}+2y&=5\\ 2y&=5\\ y&=\dfrac{5}{2}\end{aligned}
So the y-intercept is left parenthesis, 0, comma, start fraction, 5, divided by, 2, end fraction, right parenthesis.
To find the x-intercept, let's substitute start color #ff00af, y, end color #ff00af, equals, start color #ff00af, 0, end color #ff00af into the equation and solve for x:
\begin{aligned}3x+2\cdot\pink{0}&=5\\ 3x&=5\\ x&=\dfrac{5}{3}\end{aligned}
So the x-intercept is left parenthesis, start fraction, 5, divided by, 3, end fraction, comma, 0, right parenthesis.

## Practice

Problem 1
• Current
Determine the intercepts of the line graphed below.
x-intercept:
left parenthesis
comma
right parenthesis
y-intercept:
left parenthesis
comma
right parenthesis
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative seven, zero and zero, two.

Want more practice? Check out these exercises: