Line Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Line.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A perfectly straight path extending infinitely in both directions through two distinct points, with no thickness.

A perfectly straight edge that goes on forever in both directions.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A line is a perfectly straight path through two points that extends without end both ways and has no thickness.

Common stuck point: The procedure for line is the easy part; the trap is drawing a line with endpoints. Asking "Is the path straight and unending in both directions, with no endpoints?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the path straight and unending in both directions, with no endpoints?

Worked Examples

Example 1

easy
Write the equation of a line with slope m=2m = 2 and y-intercept b=−3b = -3.

Answer

y=2x−3y = 2x - 3

First step

1
Step 1: The slope-intercept form of a line is y=mx+by = mx + b.

Full solution

  1. 2
    Step 2: Substitute m=2m = 2 and b=−3b = -3.
  2. 3
    Step 3: The equation is y=2x−3y = 2x - 3.
In y=mx+by = mx + b, mm is the slope (rise over run) and bb is where the line crosses the y-axis. A line extends infinitely in both directions — every point on it satisfies this equation.

Example 2

medium
Find the slope of the line passing through points (1,3)(1, 3) and (4,9)(4, 9).

Example 3

easy
Use your finger to trace the top of a table. Is the top edge straight?

Example 4

medium
A circle has no flat edges. Is a circle made of a straight line?

Example 5

easy
How many straight lines does a rectangle have?

Example 6

medium
How many straight lines does the letter HH have?

Example 7

easy
A straight path that goes forever in BOTH directions is called a what?

Example 8

easy
Two straight lines cross each other and make an XX. Are they parallel or do they intersect?

Example 9

hard
Three things are drawn: (a) a straight path with two dots on its ends, (b) a straight path with one dot and an arrow on the other end, (c) a straight path with arrows on both ends. Name each one.

Example 10

easy
A rectangle has a top side, a bottom side, a left side, and a right side. The top and bottom never meet. What do we call the top and bottom sides?

Example 11

easy
A square has 4 sides. How many pairs of sides are parallel in a square?

Example 12

hard
A rectangle has a long side of 1212 cm and a short side of 55 cm. Two of its sides are parallel and the same length as the long side. Also, two of its sides are perpendicular to the long side. What is the total length of all 4 sides of the rectangle?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What is the slope of a horizontal line? What is the slope of a vertical line?

Example 2

hard
Line ℓ1\ell_1: y=3x+1y = 3x + 1. Line ℓ2\ell_2: y=−13x+4y = -\frac{1}{3}x + 4. Are these lines perpendicular? Justify your answer.

Example 3

easy
How far does a line extend?

Example 4

easy
A straight path that starts at one point and goes forever in one direction is called a what?

Example 5

easy
A straight path with two endpoints is called a what?

Example 6

easy
Does a line have any thickness?

Example 7

easy
Two lines in a plane never meet, no matter how far they extend. What are they called?

Example 8

easy
Two lines cross at a right angle. What are they called?

Example 9

easy
How many endpoints does a line have?

Example 10

easy
A line passes through points AA and BB. How is this line usually named?

Example 11

medium
Line 1 has slope 22. Line 2 is parallel to it. What is line 2's slope?

Example 12

medium
Line 1 has slope 33. Line 2 is perpendicular to it. Find line 2's slope.

Example 13

medium
In the equation y=mx+by = mx + b, what does bb represent for the line?

Example 14

medium
Do the lines y=2x+1y = 2x + 1 and y=2x−4y = 2x - 4 ever intersect?

Example 15

medium
A line is horizontal. What is its slope?

Example 16

medium
Why is the slope of a vertical line undefined?

Example 17

medium
Three lines are drawn so that no two are parallel and no three meet at one point. How many intersection points are there?

Example 18

medium
Order from most to fewest endpoints: line, segment, ray.

Example 19

challenge
Find the equation of the line through points (1,2)(1, 2) and (3,8)(3, 8).

Example 20

challenge
Line AA is y=12x+3y = \tfrac{1}{2}x + 3. Find the equation of the line perpendicular to AA that passes through (4,1)(4, 1).

Example 21

challenge
Find the point where the lines y=2x+1y = 2x + 1 and y=−x+7y = -x + 7 cross.

Example 22

challenge
Explain why two distinct lines in a plane can cross at most once.

Example 23

easy
Look at the two paths. One is straight like a ruler. One is wiggly like a snake. Which one is the straight line?

Example 24

easy
A square has flat edges. Are the edges of a square straight or wiggly?

Example 25

easy
A triangle has 3 flat edges. Is each edge a straight line?

Example 26

easy
Look at a big letter O. Is the O made of a straight line?

Example 27

medium
A door is shaped like a tall rectangle. Are the sides of a door straight lines?

Example 28

medium
Hold a stick. Is the stick like a straight line or like a circle?

Example 29

hard
A square has 4 flat edges. How many of those edges are straight?

Example 30

easy
A square has straight edges. How many straight lines make a square?

Example 31

easy
A triangle has 3 corners. How many straight lines make a triangle?

Example 32

easy
A hexagon has 6 sides. How many straight lines make a hexagon?

Example 33

medium
A circle has no corners and no flat sides. How many straight lines does a circle have?

Example 34

medium
A pentagon has 5 sides. How many straight lines make a pentagon?

Example 35

hard
The letter TT is drawn with straight lines. How many straight lines does TT use?

Example 36

easy
A straight path with two endpoints is called a what?

Example 37

easy
A straight path with only one endpoint that keeps going forever in the other direction is called a what?

Example 38

easy
Two straight lines on the floor look like train tracks. They never meet. What are these lines called?

Example 39

medium
How many endpoints does a line segment have?

Example 40

medium
How many endpoints does a line have?

Example 41

easy
A line segment is 77 cm long. Another line segment is 55 cm long. What is the total length if you put them end to end?

Example 42

easy
Two lines cross at a right angle (a square corner, 90∘90^\circ). What are these lines called?

Example 43

easy
A line segment ABAB is 88 cm long. A second line segment CDCD is 44 cm long. How much longer is ABAB than CDCD?

Example 44

medium
Look at the letter LL. The two line segments meet at a square corner. Are the two segments parallel or perpendicular?

Example 45

medium
Three line segments measure 66 cm, 88 cm, and 44 cm. What is the total length of all three put end to end?
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Related Concepts

PointPlane

Background Knowledge

These ideas may be useful before you work through the harder examples.

point