CLASS: JSS 2
TERM: 3rd TERM
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.
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:
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
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
y = x + 3; y = 2x – 3; y = x – 3; y = 2x + 8; y = 2x – 7; y = x – 5
WABP Essential Mathematics.AJS Oluwasanmi. Chapter 16 pg. 182 – 185
Exercise 16.3 No 5&7 page 191
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