Find the Domain y+7=4(x-3)

Problem

y+7=4*(x−3)

Solution

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

2. Isolate the variable y to express the equation as a function of x Subtract 7 from both sides.

y=4*(x−3)−7

3. Simplify the expression by distributing the 4 and combining like terms.

y=4*x−12−7

y=4*x−19

4. Determine the domain by checking for any restrictions on x Since y=4*x−19 is a polynomial (specifically a linear function), there are no denominators that could be zero and no square roots of negative numbers.

5. Conclude that the function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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