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Two-Variable Linear Graph

Simple Graphs · Class VIII

Plot a x + b y = c by isolating y. Slide a, b, c.

2
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-55
3
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-55
6
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-2020
Live values
  • x intercept (y=0)3
  • y intercept (x=0)2
  • Slope-0.6667
xy
  • y from a x + b y = c

Formulas in this lab

  • x intercept (y=0)
    ca\dfrac{c}{a}
  • y intercept (x=0)
    cb\dfrac{c}{b}
  • Slope
    −ab-\dfrac{a}{b}
Tip: Solve the equation for y and you can read off slope and intercept directly.

Frequently asked questions

▶How do I graph the equation ax + by = c?

Find two points by setting x = 0 (gives y = c/b) and y = 0 (gives x = c/a), then draw the line through them. For 2x + 3y = 6, the line passes through (0, 2) and (3, 0). The lab shows both intercepts.

▶How do I use the linear graph lab?

Slide a, b, c. The lab shows the y-intercept c/b and x-intercept c/a; plot those two points and connect to get the line. Try a = 1, b = 2, c = 4 to see intercepts at x = 4 and y = 2.

▶What does each intercept mean in real life?

If 2x + 3y = 60 means 2 kg of dal at Rs x plus 3 kg of rice at Rs y costs Rs 60, the x-intercept says dal price if rice is free, and y-intercept says rice price if dal is free. Such graphs help in budget planning and trade-offs.

▶ax + by = c vs y = mx + c: are they the same?

Both describe a straight line, but in different forms. ax + by = c is the standard form, while y = mx + c is slope-intercept form. You can convert: y = (-a/b) x + (c/b), so slope m = -a/b and intercept = c/b. The lab uses the standard form; rearrange in your notebook if needed.