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Question

Difficulty: EasyLinear Equations and Graphing

In the coordinate plane, the line representing the linear equation 3x−4y=83x - 4y = 8 contains the point (−4,b)(-4, b). What is the value of bb?

Answer: -5

Answer

The value of bb is −5-5.
Substituting the coordinates (−4,b)(-4, b) into the equation 3x−4y=83x - 4y = 8 yields 3(−4)−4b=83(-4) - 4b = 8. Simplifying gives −12−4b=8-12 - 4b = 8. Adding 1212 to both sides results in −4b=20-4b = 20. Finally, dividing by −4-4 gives b=−5b = -5.

Step-by-Step Solution

1
Substitute the point (−4,b)(-4, b) into the equation 3x−4y=83x - 4y = 8.
3(−4)−4(b)=83(-4) - 4(b) = 8
Since the point lies on the line, its coordinates must satisfy the line's equation.
2
Simplify the constant term.
−12−4b=8-12 - 4b = 8
Multiplying 33 by −4-4 yields −12-12.
3
Isolate the variable term by adding 1212 to both sides.
−4b=20-4b = 20
Adding 1212 to 88 gives 2020.
4
Solve for bb by dividing both sides by −4-4.
b=−5b = -5
Dividing 2020 by −4-4 yields −5-5.

Key Concept

Determining an unknown coordinate of a point on a line by substitution into the linear equation.
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Topics

Linear Equations and Graphing

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