Math Problem Statement

gambar grafik dari 5x+y=8

Solution

Untuk menggambar grafik dari persamaan linear 5x+y=85x + y = 8, kita bisa menulis ulang persamaan tersebut dalam bentuk y=mx+cy = mx + c untuk memudahkan plotting grafiknya:

  1. 5x+y=85x + y = 8
  2. Pindahkan 5x5x ke sisi kanan: y=5x+8y = -5x + 8

Persamaan ini menunjukkan bahwa garis memiliki kemiringan m=5m = -5 dan memotong sumbu yy di titik (0,8)(0, 8).

Sekarang saya akan menggambar grafik untuk persamaan ini.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through plotting the graph manually:

  1. Rewrite 5x+y=85x + y = 8 as y=5x+8y = -5x + 8.
  2. Choose some xx-values, for example x=0x = 0 and x=1x = 1.
    • When x=0x = 0, y=8y = 8.
    • When x=1x = 1, y=3y = 3.
  3. Plot these points (0,8)(0,8) and (1,3)(1,3) on a graph.
  4. Draw a straight line through them to complete the graph.

Would you like more information on graphing techniques, or do you have other questions?


Here are five related questions to explore further:

  1. How would the graph change if the slope were different?
  2. What is the significance of the yy-intercept in the graph?
  3. How would this line intersect the xx-axis, and at what point?
  4. What if you had a similar equation, like 5x+y=105x + y = 10?
  5. How can you check if a point lies on this line?

Tip: For linear equations, finding two points is enough to draw the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form y = mx + b

Theorems

Linear equation representation

Suitable Grade Level

Grades 6-8