7.4 The slope-intercept form of a line

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$\begin{array}{l} y = 7 x . & In this case m = 7 and b = 0 since we can write y = 7 x as y = 7 x + 0. \end{array}$

The following equations are not in slope-intercept form:

$\begin{array}{l} 2 y = 4 x - 1. & The coefficient of y is 2. \end{array} To be in slope-intercept form, the coefficient of y must be 1.$

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$\begin{array}{l} y + 4 x = 5. & The equation is not solved for y . \end{array} The x and y appear on the same side of the equal sign .$

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$\begin{array}{l} y + 1 = 2 x . & The equation is not solved for y . \end{array}$

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Practice set a

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

$\begin{matrix} y = 2 x + 7; & m = & b = \end{matrix}$

$m = 2, b = 7$

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$\begin{matrix} y = - 4 x + 2; & m = & b = \end{matrix}$

$m = - 4, b = 2$

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$\begin{matrix} y = - 5 x - 1; & m = & b = \end{matrix}$

$m = - 5, b = - 1$

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$\begin{matrix} y = \frac{2}{3} x - 10; & m = & b = \end{matrix}$

$m = \frac{2}{3}, b = - 10$

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$\begin{matrix} y = \frac{- 5}{8} x + \frac{1}{2}; & m = & b = \end{matrix}$

$m = \frac{- 5}{8}, b = \frac{1}{2}$

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$\begin{matrix} y = - 3 x; & m = & b = \end{matrix}$

$m = - 3, b = 0$

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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 $- 3$ .

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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 $x$ .

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Graph the line $y = \frac{2}{3} x + 1$ .

$x$	$y$	$(x, y)$
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 $+ 1$ .

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

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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.

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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.

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

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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 $(0, b) .$

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

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Questions & Answers

how did you get 1640

Noor Reply

If auger is pair are the roots of equation x2+5x-3=0

Peter Reply

Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.

MATTHEW Reply

420

Sharon

from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph

George

Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28

Salma

Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.

Aaron Reply

find product (-6m+6) ( 3m²+4m-3)

SIMRAN Reply

-42m²+60m-18

Salma

what is the solution

bill

how did you arrive at this answer?

bill

-24m+3+3mÁ^2

Susan

i really want to learn

Amira

I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please

Amira

Hw did u arrive to this answer.

Aphelele

Bajemah

-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18

Salma

complete the table of valuesfor each given equatio then graph. 1.x+2y=3

Jovelyn Reply

x=3-2y

Salma

y=x+3/2

Salma

Enock

given that (7x-5):(2+4x)=8:7find the value of x

Nandala

3x-12y=18

Kelvin

please why isn't that the 0is in ten thousand place

Grace Reply

please why is it that the 0is in the place of ten thousand

Grace

Send the example to me here and let me see

Stephen

A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg

Marry Reply

how far

Abubakar

cool u

Enock

state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°

Abegail Reply

hello

BenJay

Method

I am eliacin, I need your help in maths

Rood

how can I help

Sir

hmm can we speak here?

Amoon

however, may I ask you some questions about Algarba?

Amoon

Enock

what the last part of the problem mean?

Roger

The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.

cameron Reply

Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.

mahnoor Reply

I'm guessing, but it's somewhere around $4335.00 I think

Lewis

12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00

Munster

difference between rational and irrational numbers

Arundhati Reply

When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?

Jakoiya Reply

how to reduced echelon form

Solomon Reply

Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?

Zack Reply

d=r×t the equation would be 8/r+24/r+4=3 worked out

Sheirtina

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Source: OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3

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