**SUBJECT: MATHEMATICS**

**CLASS: JSS 2**

**DATE:**

**TERM: 3rd TERM**

**REFERENCE**

- WABP ESSENTIAL MATHEMATICS FOR JSS BK 2 BY A.J.S. OLUWASANMI
- NEW GENERAL MATHEMATICS BY J.B. CHANNON & ETAL

WEEK TWO

**TOPIC: GRAPHS OF LINEAR EQUATIONS**

**CONTENT: **** ****(i) Equations and table of values**

** **** ****(ii) Plotting points from the table of values**

** **** ****(iii) General form of linear equations **

**Equations and Table of Values**

y = 2x – 5 is an equation of x and y. the equation connects the two variables x and y so that for any value of, there is a corresponding value of y. For example if x = 3, then y = 1 and if x = -2, y = -9. Table below is a table of values that shows corresponding values of the variables x and y for the equation y = 2x – 5. We say that y is the dependent variable since the value of y depends on the value of x. c is the independent variable.

x | -2 | -1 | 0 | 1 | 2 | 3 | 4 |

2x | |||||||

-5 | |||||||

y = 2x - 5 |

**Evaluation:**Copy and complete the table above.

**Plotting Points Fromthe Table of Values:**

Table above contains the following set of ordered pairs of corresponding values of x and y. (-2, -9), (-1, -7), … These ordered pairs are equivalent to a set of coordinates of points that can be plotted on the Cartesian plane. y = 2x – 5 is a linear equation in x and the variables in a linear equation are always separate and have a power of 1 (i.e. there are no terms such as xy, x2, y3 etc.). The graph of a linear equation is always a straight line. In general, a straight line has an equation in the form y = mx + c, where x and y are variables and m and c are constants.

**Evaluation:**Draw the graph of y = 4x – 7 for values of x from -3 to +3. From your graph find:

- The value of y when x = 2.5
- The value of x when y = -1.3
- The coordinates of the points where the line cuts the axes.

**General Form of Linear Equations:**

The general form for the equation of a straight line is y = mx + c. Where m and c are constants.mis the coefficient of x and it is often called the gradient of the line. c is called the intercept on the y-axis. When a linear equation is given in this form, the values of m and c can easily be obtained. As shown below.

If y = -5x – 4, then m = -5 and c = -4

ax + by + c = 0 is another form of equation of a line. Notice that the terms are in alphabetical order. Where a, b and c are constants.

For example: 3x – 2y – 10 = 0 is in the form ax + by + c = 0, where a = 3, b = -2, and c = -10

To obtain m and c in the above equation, there is need to convert it to the form y = mx + c

**Example: **Find the values of m and c in the equation 2x – y + 7 = 0

**Solution: **

Given: 2x – y + 7 = 0, add y to both sides

2x + 7 = y

i.e. y = 2x + 7 (in the form y = mx + c)

Thus, m = 2 and c = 7

**Evaluation: **

- The equations of six straight lines are:

y = x + 3; y = 2x – 3; y = x – 3; y = 2x + 8; y = 2x – 7; y = x – 5

- Which of these lines are parallel?
- Write down the values of m and c, where m is the gradient and c is the intercept on the y-axis.

**GENERAL EVALUATION**

- Draw the graph of y = 3x – 4 for values of x from -2 to 2
- Write down the coordinates of the points where the graph cuts the y-axis

**REVISION QUESTION**

- Draw the graph of y = -5 – 3x for -4 x 3
- Find the coordinates of the points where the line cuts the axes.

**READING ASSIGNMENT**

WABP Essential Mathematics.AJS Oluwasanmi. Chapter 16 pg. 182 – 185

Exercise 16.3 No 5&7 page 191

**WEEKEND ASSIGNMENTS**

- Given that y = 3x – 5, find m A. -5 B. -3 C. 3 D. 5
- If y = -2x + 7, find c A. -2 B. 7 C. 2 D. -7
- Given an equation of a straight line: 2y + 6x – 10 = 0, find the gradient A. 6 B. 3 C. -6 D. -3
- In question (3) above, find the intercept on the y-axis A. 2 B. 6 C. -10 D. 5
- Given the equations (i) y = 2x – 3, (ii) y = x + 3 and (iii) y = 2x + 8. Which of these are parallel? A. i and iii B. i and iii C. ii and iii D. i, ii and iii

**THEORY**

- Draw the graphs of the functions y + 3x – 4 and x – y = 5 on the same axes. Write down the coordinates of the point where both lines intersect.
- Find the x and y intercepts of the following lines a. 3x – 9 = 2y b. 2y – x + 3 = 0

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