Question

work 12 in week 7: the coordinate plane
question 1, 2.1.17
hw score: 0%, 0 of 12 points
part 1 of 7
points: 0 of 1
plot the points (5,0), (5 - 4), (5,4), (5,8), and (5 - 3). describe the set of all points of the form (5,y), where y is a real number
plot the point (5,0)

Explanation:

Step1: Recall the coordinate - plane concept

In a two - dimensional coordinate plane, a point is represented as \((x,y)\). For the set of points \((5,y)\) where \(y\in R\) ( \(R\) is the set of all real numbers), the \(x\) - coordinate is fixed at \(x = 5\).

Step2: Analyze the nature of the set of points

The equation of a vertical line in the coordinate plane is of the form \(x=a\), where \(a\) is a constant. Here, since \(x = 5\) for all points \((5,y)\) and \(y\) can take any real - value (\(y\in(-\infty,\infty)\)), the set of points \((5,y)\) forms a vertical line.

Answer:

The set of all points of the form \((5,y)\) where \(y\) is a real number is a vertical line passing through the point \((5,0)\) with the equation \(x = 5\).