Rope-Line RoryGridwalkers · the coordinate plane, slope and lines

Stretches a taut rope between two pegs: writing the equation of a line.

Equation of a Line

Writing the equation of a line. In MathBound, the free Algebra I adventure game, Rope-Line Rory asks these problems, and the only way past is to solve them.

Part of Linear Functions: chapter 5 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Given Slope and y-intercept. Write the equation of a line given an integer slope and y-intercept.
Given Slope and a Point.
Given Two Points.
Parallel Lines.
Perpendicular Lines.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Given Slope and y-intercept

Find

the

equation

of

the

line

with

slope

- 4

and

y -intercept

(0, - 8) .

$y = - 8 x - 4$
$y = - 8$
$y = - 4 x$
$y = - 4 x - 8$

Show the worked steps

$Slope-intercept$ $form$ $is$ $y = m x + b .$
$That$ $gives$ $y = - 4 x - 8 .$

Answer: $y = - 4 x - 8$

Example 2 · Given Slope and a Point

A

taxi

charges

$5

for

each

mile

plus

a

fixed

fee.

A

7 - mile

ride

costs

$37 .

Which

equation

gives

the

cost

y

of

an

x -mile

ride?

$y = 5 x + 37$
$y = 5 x + 2$
$y = 37 x + 5$
$y = 5 x + 30$

Show the worked steps

$The$ $slope$ $is$ $the$ $rate,$ $5,$ $and$ $(7, 37)$ $is$ $on$ $the$ $line.$
$37 = 5 (7) + b,$ $so$ $b = 2 : y = 5 x + 2 .$

Answer: $y = 5 x + 2$

Example 3 · Given Two Points

Find

the

equation

of

the

line

through

(2, 7)

and

(3, 10) .

$y = 3 x + 7$
$y = x + 1$
$y = - 3 x + 1$
$y = 3 x + 1$

Show the worked steps

$Slope$ $= \frac{10 - 7}{3 - 2} = 3 .$
$Then$ $b = 1,$ $giving$ $y = 3 x + 1 .$

Answer: $y = 3 x + 1$

Where it is in your textbook

Textbook	Lessons
Standard course	5.3, 5.4, 5.6
Big Ideas Math Algebra 1	4.1, 4.2, 4.3
Big Ideas Math Algebra 1 (2022)	4.1, 4.2, 4.3
Carnegie Learning Algebra I	M2 1.2, M2 1.4
CPM Core Connections Algebra	2.2.1, 2.2.3, 2.3.1, 2.3.2, 6.1.4
CPS Skyline Algebra	2.9, 2.10, 8.1-8.2
enVision Algebra 1	2-1, 2-2, 2-4
enVision Algebra 1 (2024)	2-1, 2-2, 2-4
Eureka Math Algebra I (EngageNY)	2.14, 5.3, 5.4
Glencoe Algebra 1	3-6, 4-1, 4-2, 4-4
HMH Into Algebra 1	4.2, 4.4
Holt McDougal Larson Algebra 1	4.1, 4.2, 4.5
Illustrative Mathematics Algebra 1	3.4-3.5, 4.18
Illustrative Mathematics Algebra 1 (v.360)	2.18-2.19, 3.4-3.5, 5.18
Math Nation Algebra 1 (Florida B.E.S.T.)	3.2, 3.3, 3.4, 4.10, 4.11, 4.12
MVP Mathematics I (Integrated Math 1)	2.10, 2.11, 8.3
Open Up NC Math 1 (MVP)	2.8, 2.9, 8.3
OpenStax Elementary Algebra 2e	4.6
Pearson Algebra 1 Common Core	4-2, 4-5, 5-3, 5-4, 5-6
Reveal Algebra 1	4-3, 5-1
SpringBoard Algebra 1	12, 15, 34

Ready for Rope-Line Rory?

Play this battle free Play the whole adventure