Question

so far you have graphed relationships where y changes as x increases. what happens when the value of y stays the same? plot five points with a y - coordinate of 3.

Explanation:

Step1: Understand the coordinate system

In a coordinate system, a point is represented as \((x,y)\). Here, \(y = 3\) (given), and \(x\) can be any real - number.

Step2: Choose values for \(x\)

Let's choose \(x=-3\), \(x = - 1\), \(x=0\), \(x = 1\), \(x=3\)

The points will be \((-3,3)\), \((-1,3)\), \((0,3)\), \((1,3)\), \((3,3)\)

Step3: Plot the points

On the given coordinate plane:

• For the point \((-3,3)\): Move 3 units to the left of the origin along the \(x\) - axis and 3 units up along the \(y\) - axis.
• For the point \((-1,3)\): Move 1 unit to the left of the origin along the \(x\) - axis and 3 units up along the \(y\) - axis.
• For the point \((0,3)\): Move 0 units along the \(x\) - axis (stay on the \(y\) - axis) and 3 units up along the \(y\) - axis.
• For the point \((1,3)\): Move 1 unit to the right of the origin along the \(x\) - axis and 3 units up along the \(y\) - axis.
• For the point \((3,3)\): Move 3 units to the right of the origin along the \(x\) - axis and 3 units up along the \(y\) - axis.

When \(y\) stays the same (constant), the set of points \((x,y)\) forms a horizontal line. In this case, the equation of the line is \(y = 3\)

Answer:

The five points are \((-3,3)\), \((-1,3)\), \((0,3)\), \((1,3)\), \((3,3)\) and when \(y\) is constant, the points form a horizontal line \(y = 3\)