Mathematics (VII)

Abdullah Al Mahmud

Chapter 7.3 (Graphs)

What We Learn from This Plot

Coccept of graph

Imagine you are at your home. You came out and went 10m eastward and 5m southward. Where is you current location?

  • This point is called (10,5)

Know this man?

Quadrants and Axes

Where would these points be?

Mention that “lengths of the side of the smallest square as unit along both axes.”

  • (10,2)
  • (-10,2)
  • (10,-5)
  • (-10,-5)

Put on graph paper

  • A (5,3)
  • B (5,-3)
  • C (-5,3)
  • D (-5,-3)

Find the geometric shape from this coordinates

  1. (3,2); (6,2); (6,4); (3,4)
  2. (0,4); (2,2); (4,0)
  3. (2,0); (3,4); (4,0)

Draw these points. What are the shapes?

Plotting an Equation

y = 3x + 5

If x = 2, 3, 4, 5

\(y=3 \times 2 + 5 = 11\)…

Solving Equation with Graph

First solve manually

  1. Solve and show solutions using graphs
  1. x-4=0
  2. 2x+1 = x-3
  • Classwork: 3x+4 = 5x

Solve by Graph

5x+4 = 4x + 7; without solving mathematically

Exercise 7.3 (14)

Length of three sides of a triangle are (x+2), (x+4), and (x+6) cm (x>0). Perimeter of the triangle is 18 cm.

  1. Draw a proportional figure using the conditions.
  2. Formulate and solve.
  3. Draw the graph of the solution.

Exercise 7.3 (15)

Distance between Dhaka and Aricha is 77 km. A bus starts from Dhaka to Aricha at 30 kmh, and another from Aricha to Dhaka at 40 kmh. The two meet at x km from Dhaka.

  1. How far from Aricha will they meet? Express in terms of x.
  2. Determine x
  3. How much time will each bus take to reach their destinations?

Extra Exercise 01

Solve

\(5x^2+6x+18=4x^2+9\)

  • \(x^2+5x+6=0\)