<< 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!

Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

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