Straight-Line Graphs

What you’ll learn

Interpret a line’s gradient and vertical intercept.

បកស្រាយមេគុណប្រាប់ទិស និងចំណុចកាត់អ័ក្សឈរ។

Meaning and use

The equation y = mx + b describes a nonvertical straight line. The gradient is the change in y divided by the change in x. The intercept b is the value of y when x is zero. A vertical line cannot be written in this form with a finite gradient.

ក្នុង y=mx+b មេគុណ m បង្ហាញបម្រែបម្រួល y ធៀប x។ b ជាតម្លៃ y ពេល x=0។ បន្ទាត់ឈរមានរូបរាងខុសពីទម្រង់នេះ។

Formulas

Line and gradient

\[y=mx+b,\qquad m=\frac{y_2-y_1}{x_2-x_1}\]

Vertical intercept

\[x=0\quad\Longrightarrow\quad y=b\]

Symbols and units

Symbol	Meaning	Unit or restriction
x, y	Coordinates	Axis units, if given
m	Gradient	y-unit per x-unit
b	Vertical intercept	y-unit

Conditions and limits

• For the two-point formula, x₂ must differ from x₁.
• Subtract coordinates in the same order in numerator and denominator.
• ប្រយ័ត្នមាត្រដ្ឋានអ័ក្ស មិនត្រូវរាប់តែក្រឡាដោយមិនមើលឯកតាទេ។

Worked examples

Reading a line equation

For \(y=2x+3\), find y when x = 4.

1. Substitute \(x=4\).
2. Calculate \(y=2(4)+3=11\).

y = 11

ដាក់តម្លៃ x ក្នុងសមីការ ហើយគោរពលំដាប់ប្រមាណវិធី។

Gradient from points

Points are (1, 3) and (4, 9).

1. Change in y is \(9-3=6\).
2. Change in x is \(4-1=3\).
3. Gradient \(m=6/3=2\).

m = 2

គិតបម្រែបម្រួល y ចែកបម្រែបម្រួល x។

Common mistakes

Instead of	Use	Why
Gradient = change in x / change in y.	Gradient = change in y / change in x.	The order defines the line’s slope.
In y = 2x + 3, the vertical intercept is 2.	The vertical intercept is 3.	Set x to zero to check.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. For y = 3x − 2, find y when x = 5.
2. Find the gradient through (0, 1) and (2, 5).
3. What is the vertical intercept of y = −x + 4?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 13

   3 × 5 − 2 = 13.

2. 2

   (5 − 1)/(2 − 0) = 4/2.

3. 4

   At x = 0, y = 4.

Quick recap

• Gradient is rise divided by run.
• The intercept is y at x = 0.
• Handle vertical lines separately.