Mastering Slope-Intercept Form

a The

y -

intercept and the slope of the line need to be determined to write the equation of the line in slope-intercept form. Begin by remembering slope-intercept form of a line.

y = m x + b

In this form,

m

is the slope and

b

is the

y -

intercept. The

y -

intercept of a line is the

y -

coordinate of the point where the line crosses the

y -

axis.

In the given graph, the line intercepts the

y -

axis at

(0, 100000) .

This means that the

y -

intercept of the line is

100000 .

Substitute

100000

for

b

into the slope-intercept form of an equation.

y = m x + b ⇓ y = m x + 100000

The slope of a line is the ratio of the rise and run of the line.

m = \frac{rise}{run}

Any two points on the line can be chosen to determine the rise and run. One point can be the one where the line intercepts the

y -

axis. The other point can be

(50, 60000)

for simplicity.

The rise is

- 40000

and the run is

50 .

Substitute these values into the ratio and calculate the slope.

m = \frac{rise}{run}

SubstituteII

$rise = - 40000$ , $run = 50$

m = \frac{- 4 0 0 0 0}{5 0}

MoveNegNumToFrac

Put minus sign in front of fraction

m = - \frac{4 0 0 0 0}{5 0}

CalcQuot

Calculate quotient

m = - 800

The slope of the line is

- 800 .

Finally, the equation of the line can be completed by substituting

- 800

for

m .

y = m x + 100000 ⇓ y = - 800 x + 100000

b Remember the equation from Part A.

y = - 800 x + 100000

The slope of the line is negative, which suggests that the number of cheetahs decreases by

800

per year. The

y -

intercept represents that there were

100000

cheetahs in

1900 .

c In the equation,

y

represents the number of cheetahs after

x

years. Substitute

0

for

y

into the equation and solve for

x

to find after how many years cheetahs will go extinct, according to the graph.

y = - 800 x + 100000

Substitute

$y = 0$

0 = - 800 x + 100000

AddEqn

$LHS + 800 x = RHS + 800 x$

800 x = 100000

DivEqn

$LHS / 800 = RHS / 800$

\frac{8 0 0 x}{8 0 0} = \frac{1 0 0 0 0 0}{8 0 0}

CalcQuot

Calculate quotient

x = 125

The equation suggests that cheetahs will go extinct after

125

years. The specific year can be found by adding

125

to the starting year

1900 .

1900 + 125 = 2025

This means that if the current trend continues, cheetahs will go extinct in

2025 .

Number of Days $x$	$5$	$9$	$15$
Number of Pages $y$	$147$	$95$	$17$

Number of Days

x

5

9

15

Number of Pages

y

147

95

17

Number of Days $x$	$5$	$9$	$15$
Number of Pages $y$	$147$	$95$	$17$
Point $(x, y)$	$(5, 147)$	$(9, 95)$	$(15, 17)$

Number of Days

x

5

9

15

Number of Pages

y

147

95

17

Point

(x, y)

(5, 147)

(9, 95)

(15, 17)

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Catch-Up and Review

Deriving the Equation for a Nonproportional Relationship

Analyzing Graphs of Equations

Points Where a Line Crosses the Axes

Intercept

Finding the Intercepts of a Line

Linear Equation

Slope-Intercept Form

Identifying Slope-Intercept Form

Graphing a Linear Equation in Slope-Intercept Form

Following the Fish Population

Answer

Hint

Solution

Writing the Equation of a Line in Slope-Intercept Form From a Graph

Chasing the Big Cats

Answer

Hint

Solution

Writing the Equation of a Line in Slope-Intercept Form Using Two Points

Reading the Research Rag

Hint

Solution

Writing Equations in Slope-Intercept Form

Determining the Slope and y-Intercept of a Line

Equation of a Nonproportional Relationship

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