<< Chapter < Page Chapter >> Page >

y = 7 x . In this case m = 7 and b = 0 since we can write y = 7 x as y = 7 x + 0.

Got questions? Get instant answers now!

The following equations are not in slope-intercept form:

2 y = 4 x 1. The coefficient of y is 2. To be in slope-intercept form, the coefficient of y must be 1.

Got questions? Get instant answers now!

y + 4 x = 5. The equation is not solved for y . The x and y appear on the same side of the equal sign .

Got questions? Get instant answers now!

y + 1 = 2 x . The equation is not solved for y .

Got questions? Get instant answers now!

Practice set a

The following equation are in slope-intercept form. In each case, specify the slope and y -intercept .

y = 2 x + 7 ; m = b =

m = 2 , b = 7

Got questions? Get instant answers now!

y = 4 x + 2 ; m = b =

m = 4 , b = 2

Got questions? Get instant answers now!

y = 5 x 1 ; m = b =

m = 5 , b = 1

Got questions? Get instant answers now!

y = 2 3 x 10 ; m = b =

m = 2 3 , b = 10

Got questions? Get instant answers now!

y = 5 8 x + 1 2 ; m = b =

m = 5 8 , b = 1 2

Got questions? Get instant answers now!

y = 3 x ; m = b =

m = 3 , b = 0

Got questions? Get instant answers now!

Slope and intercept

When the equation of a line is written in slope-intercept form, two important properties of the line can be seen: the slope and the intercept . Let's look at these two properties by graphing several lines and observing them carefully.

Sample set b

Graph the line y = x 3 .

x y ( x , y )
0 3 ( 0 , 3 )
4 1 ( 4 , 1 )
2 5 ( 2 , 5 )

A graph of a line passing through three points with coordinates zero, negative three; four, one , and negative two, negative five.

Looking carefully at this line, answer the following two questions.

At what number does this line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at - 3 .

Got questions? Get instant answers now!

Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

After moving horizontally one unit to the right, we must move exactly one vertical unit up. This number is the coefficient of x .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph the line y = 2 3 x + 1 .

x y ( x , y )
0 1 ( 0 , 1 )
3 3 ( 3 , 3 )
3 1 ( 3 , 1 )

A graph of a line passing through three points with coordinates zero, one; three, three, and negative three, negative one.

Looking carefully at this line, answer the following two questions.

At what number does this line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at + 1 .

Got questions? Get instant answers now!

Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

After moving horizontally one unit to the right, we must move exactly 2 3 unit upward. This number is the coefficient of x .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Practice set b

Graph the line y = 3 x + 4 .

x y ( x , y )
0
3
2

An xy coordinate plane with gridlines, labeled negative five and five on the both axes.

Got questions? Get instant answers now!

Looking carefully at this line, answer the following two questions.

At what number does the line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at + 4 . After moving horizontally 1 unit to the right, we must move exactly 3 units downward.

Got questions? Get instant answers now!

Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

A graph of a line passing through two points with coordinates zero,four; two, negative two ,and three, negative five.

Got questions? Get instant answers now!

In the graphs constructed in Sample Set B and Practice Set B, each equation had the form y = m x + b . We can answer the same questions by using this form of the equation (shown in the diagram).

A graph of a line sloped up and to the right in a first quadrant labeled with the equation y equal to mx plus b and intersecting y axis at point with coordinates zero, b. Lines illustrating an upward change of m units and a horizontal change of one unit to the right.

y -intercept

At what number does the line cross the y -axis ? Do you see this number in the equation?

In each case, the line crosses the y -axis at the constant b . The number b is the number at which the line crosses the y -axis , and it is called the y -intercept . The ordered pair corresponding to the y -intercept is ( 0 , b ) .

Got questions? Get instant answers now!

Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

To get back on the line, we must move our pencil exactly m vertical units.

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask