The x- and y-intercepts of a graph

The x-intercept of a graph is that point where the graph crosses the x-axis.  The y-intercept is where it crosses the y-axis.

Example 2.   Mark the x- and y-intercepts, and sketch the graph of

5x − 2y  =  10

Solution.   Although this does not have the form  y = ax + b, the strategy is the same.  Find the intercepts by putting x -- then y -- equal to 0.

When we put x = 0, we have

When we put y = 0, we have

Here is the graph:

Problem 13.

a)  In an equation  y = ax + b , where on the graph do we find b ?

As the y-intercept.

b)  Where do we find the solution to  ax + b = 0 ?

As the x-intercept.

Problem 14.   Mark the x− and y−intercepts, and draw the graph.

a)	y = 2x − 6		b)	y = −3x + 3
c)	y = 4x + 2		d)	x − y = 3
				See Example 2.
e)	x − 2y + 2 = 0		f)	2x − 3y − 6 = 0
g)	y = −x + 1		h)	y = 6x − 3

Problem 15.   The form  y = ax.   

a)   When an equation has the form  y = ax  (for example,  y = 2x),  what
a)   number is b ?   0

b)   Therefore, what number is the y-intercept?   0

c)   Through which point does the line pass?

The origin. In other words the x- and y- intercepts coincide.

d)   How do we find another point on the line?

Choose any value for x. The equation will then determine the value of y.

Example 6.   Lines parallel to the axes.

An equation of the form

x  =  A number

is a straight line parallel to the y-axis.  For example,

x  =  3

The x-coordinate of every point on that line is 3.

An equation of the form

y  =  A number

is a straight line parallel to the x-axis.  For example,

y  =  −4

The y-coordinate of every point on that line is −4.

Problem 17.   Sketch each graph.

a)	x = 5		b)	x = −2
c)	y = 3		d)	y = −1

Problem 18.

a)   What is the equation of the x-axis?   y = 0

b)   What is the equation of the y-axis?   x = 0