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๐Ÿ“‹ Algebra 1 Formula Reference Sheet

Frisco ISD ยท Unit 2B ยท Linear Equations & Functions  |  Keep this handy while practising!

โ‘  Slope-Intercept Form
y = mx + b
m = slope (steepness / rate of change)
b = y-intercept (where line crosses y-axis)
Example
y = 3x + โˆ’5  โ†’  slope = 3, y-int = โˆ’5
โ‘ก Standard Form
Ax + By = C
A must be positive (no fractions)
Used to find intercepts quickly
Example
3x + 4y = 24  โ†’  A=3, B=4, C=24
โ‘ข Slope Formula (Two Points)
m = (yโ‚‚ โˆ’ yโ‚) รท (xโ‚‚ โˆ’ xโ‚)
Also written as: rise รท run = ฮ”y รท ฮ”x
Example: points (1, 3) and (4, 9)
m = (9โˆ’3) รท (4โˆ’1) = 6 รท 3 = 2
โ‘ฃ Finding Intercepts

x-intercept

  • Set y = 0
  • Solve for x
  • Write as (x, 0)

y-intercept

  • Set x = 0
  • Solve for y
  • Write as (0, y)
โ‘ค Converting Between Forms
Slope-Intercept โ†’ Standard Form
  • If fractions: multiply all terms by the denominator
  • Move the x-term to the left side
  • If A is negative, multiply everything by โˆ’1
y = ยฝx โˆ’ 3 โ†’ (ร—2) โ†’ 2y = x โˆ’ 6 โ†’ x โˆ’ 2y = 6
Standard Form โ†’ Slope-Intercept
  • Move the x-term to the right side
  • Divide every term by the coefficient of y
  • Simplify fractions
4x + 2y = 10 โ†’ 2y = โˆ’4x+10 โ†’ y = โˆ’2x + 5

๐Ÿ“– Key Vocabulary

Slope (m)How steep a line is. Positive = rises left to right. Negative = falls left to right. Zero = horizontal. Undefined = vertical.
y-intercept (b)The point where the line crosses the y-axis. Always in the form (0, b).
x-interceptThe point where the line crosses the x-axis. Always in the form (a, 0).
Rate of changeSame as slope in real-world problems. How much y changes for every 1 unit increase in x.
Linear equationAn equation whose graph is a straight line. Highest power of x and y is 1.

๐ŸŽต Did You Know? โ€” Len Kagamine & Maths

Hatsune Miku was created on August 31, 2007 โ€” that's the 243rd day of the year. Kagamine Len & Rin were released on December 27, 2007, exactly 118 days later. If you graphed "days since Miku's release" (x) against "new Vocaloid releases" (y), you'd have a linear equation! The slope would tell you how fast the Vocaloid family was growing. ๐ŸŽค