Find the Domain y-8=5/3*(x-5)

Problem

y−8=5/3*(x−5)

Solution

1. Identify the type of equation. The given equation is a linear equation in point-slope form, which can be rewritten in the slope-intercept form y=m*x+b

2. Isolate the variable y to express the equation as a function of x Add 8 to both sides of the equation.

y=5/3*(x−5)+8

3. Simplify the expression by distributing the fraction and combining like terms.

y=5/3*x−25/3+24/3

y=5/3*x−1/3

4. Analyze the resulting function ƒ(x)=5/3*x−1/3 This is a polynomial function of degree 1 (a linear function).

5. Determine the domain. Polynomial functions are defined for all real numbers because there are no denominators containing x that could be zero and no even roots of negative numbers.

6. Express the domain in interval notation. Since x can be any real number, the domain is (−∞,∞)

Final Answer

Domain:(−∞,∞)

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