Graphs of Linear Equation ax + by = c
Given a linear equation in x and y for example 3x + 2y = 1,
we can substitute random values of x and y, for example x = 1 and y = 1 to the left hand side,
to obtain 3(1) + 2(1) which adds to 5.
But this is not equal to 1, which is the right side of the equation.
So if the left side is not equal to the right side, then the pair of x and y values we chose do not satisfy the conditions of the equation. The pair of x and y values is not a solution to the equation!
If x = 1 and y = -1 the 3(1) + 2(-1) = 1 which equals 1 on the right hand side of the equation
In this case, the pair of x and y values substituted into the left hand side of the equation, equals to the right hand side, and satisfies the condition of the equation.
This means that the pair of x and y values is a solution to the equation.
Instead of randomly picking x and y values to satisfy the equation, we can actually substitute the value of x first and then obtain the value of y from the equation.
So for x = 1, we get 3(1) + 2y = 1
2y = 1 -3
2y = -2
y = -2/2
y = -1
So x = 1 and corresponding value of y = -1 satisfy the equation as before
If x = 3, substituting it into the equation gives 3(3) + 2y = 1
2y = 1-9
y = -8/2 = -4
So another pair of x, y values which satisfy the equation is x = 3, y = -4
Each pair of x and y values can form the x and y coordinates of a point.
The two pairs of x and y values together with numerous other pairs of x and y satisfying the equation form points on a cartesian coordinate graph. All the points satisfying the equation forms a straight line graph.
In the interactive resource below, a linear equation is presented, fill in the correct corresponding values of y and x for the given values of x and y.
Try a few linear equations in two variables (use x and y as variables) such as
(i) x + y = - 3
(ii) 3x + 2y = 0
(iii) 5x + 10y = 15
(iv) 6x - 4y = 8