Algebra 1 Common Core Student Edition, Grade 8-9

You can write th e eq u a tio n of a line given any two points on th e line. First use the

two given points to find th e slope. Then u se th e slope an d one of the points to write

the equation.

Pl an
How does the graph
help you w rite an
equation?
You can use tw o points
on the line to find the
slope. Then use
point-slope form.

Pr o b l em 3 Using Two Points to W rite an Equation

What is an equation of the line at the right?

. - T h i n k W c l! ®
You need the slope m, y2 - yi
so sta rt w ith the slope h i = x _ x
form ula.

Use th e given p oin ts to -3-4 -7 _ 7

find the slope. — 2 — 1 —3 ~ 3

Use point-slope form. y - y i = m ( x - X j)

/..

Use either given p o in t fo r _j

For exam ple, you y — 4 _ - ( X - 1)

can use (1, 4).

4 A yd

rdA)

I^1

X

—L fo 1

'

A

Pl an

How does the table

help you w rite an

equation?

The table gives four

points. You can use any

tw o of the points to

find the slope. Then use

point-slope form.

© G o t It? 3. a. In th e last step of P roblem 3, u se th e p o in t (—2, - 3 ) instead of (1,4) to

write a n e q u a tio n of the line,

b. Reasoning Rewrite the equations in Problem 3 and part (a) in

slope-intercept form. Compare the two rewritten equations. What

can you conclude?

Using a Table to W rite an Equation

Recreation The table shows the altitude of a hot-air balloon

during its linear descent. What equation in slope-intercept form

gives the balloon’s altitude at any time? What do the slope and

y-intercept represent?

Use tw o points, such as (10, 640) and

(30, 590), to fin d the slope.

Use p o in t-s lo p e form.

Use th e d ata p o in t (10, 640) and the

slope -2 .5.

Rewrite in slope-intercept form.

m = 590 - 640— r? r = “ 2.5

30 - 10

y - y l = m { x - x{j

y- 640 = — 2.5(x — 10)

y = —2.5x + 665

Hot-Air Balloon Descent

10

30

640

590

(^70490)
90 440
The slope - 2 .5 rep resen ts th e rate of desc en t of th e balloon in m eters p e r second.
The y-intercept 665 rep resen ts th e initial altitude of th e balloon in m eters.
c
PowerAlgebra.com | Le s s o n 5 - 4 Po i n t - Sl o p e Fo r m^317