4x+5y=18

Here are common ways to handle 4x + 5y = 18.

• Solve for y (slope-intercept form): y = (18 − 4x)/5 = −(4/5)x + 18/5 Slope m = −4/5, y-intercept = (0, 18/5)

• Intercepts:

  • x-intercept (y = 0): 4x = 18 ⇒ x = 9/2, so (9/2, 0)
  • y-intercept (x = 0): y = 18/5, so (0, 18/5)

• Integer solutions (if you want integer pairs (x, y) that satisfy the equation): For integers, 18 − 4x must be a multiple of 5. Since 4 ≡ −1 (mod 5), we need x ≡ 2 (mod 5). General integer solutions: x = 2 + 5t, y = 2 − 4t, where t ∈ Z. Example: t = 0 → (2, 2); t = 1 → (7, −2).

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