# Lesson Notes By Weeks and Term - Junior Secondary School 2

GRAPHS OF LINEAR EQUATIONS

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:

1. The value of y when x = 2.5
2. The value of x when y = -1.3
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:

1. 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

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

GENERAL EVALUATION

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

REVISION QUESTION

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

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

Exercise 16.3 No 5&7 page 191

WEEKEND ASSIGNMENTS

1. Given that y = 3x – 5, find m    A. -5        B. -3       C. 3        D. 5
2. If y = -2x + 7, find c     A. -2       B. 7       C. 2      D. -7
3. Given an equation of a straight line: 2y + 6x – 10 = 0, find the gradient   A. 6    B. 3     C. -6     D. -3
4. In question (3) above, find the intercept on the y-axis    A. 2     B. 6     C. -10     D. 5
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

1. 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.
2. Find the x and y intercepts of  the following lines  a. 3x – 9 = 2y     b. 2y – x + 3 = 0