Final answer:
To create a shape with all the designated equations, we utilize a combination of a horizontal line (y = 2), a vertical line (x = -1), a slope-intercept equation (y = 3x + 9), a standard line equation (-3x + y = 9), and a point-slope equation (y - 18 = 3(x - 3)), with a restriction on the domain for the horizontal line (x > -1).
Step-by-step explanation:
To create a shape that satisfies these requirements, let's start by defining each equation that we need:
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- A horizontal line equation could be y = 2.
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- A vertical line equation could be x = -1.
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- A slope-intercept equation, considering the given slope of 3 and a y-intercept of 9, would be y = 3x + 9.
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- A standard equation of a straight line that has a negative slope and passes through the same y-intercept could be -3x + y = 9.
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- For the point-slope equation, assume we have a point on this line, say (3, 18). The equation would be y - 18 = 3(x - 3).
To restrict the domain or range, we could say the horizontal line y = 2 only exists for x values greater than -1, e.g., for x > -1.
This collection of equations can be graphed to visualize their intersection points and understand the constraints on the domain or range. These are fundamental concepts outlined in sections that discuss the Algebra of Straight Lines and considerations in Graphical Analysis of One-Dimensional Motion.