The group of ordered pairs on the given line are (0, -3) and ([tex]\frac{6}{5}[/tex], 0)
Given the following equation;
[tex]5x - 2y = 6[/tex]
To find the group of ordered pairs that are on the line;
We would assume a value for the point on the x and y axis respectively.
When x = 0
Substituting the value of x into the equation;
[tex]5(0) - 2y = 6\\\\-2y = 6\\\\y = \frac{6}{-2}[/tex]
y = -3
When y = 0
Substituting the value of y into the equation;
[tex]5x - 2(0) = 6\\\\5x = 6\\\\x = \frac{6}{5}[/tex]
Therefore, the group of ordered pairs on the line are (0, -3) and ([tex]\frac{6}{5}[/tex], 0)
Check:
[tex]5x - 2y = 6[/tex]
When (x, y) = (0, -3)
[tex]5(0) - 2(-3) = 6\\\\0 + 6 = 6\\\\6 = 6[/tex]
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