Question

1. a line is parallel to the x - axis and passes through the point (3,7).

(a) plot the point (3,7) and draw the line on the grid given.
(b) plot another point that lies on the line and state its coordinates below.
(c) what is the equation of the line you drew?

Explanation:

Part (a)

To plot the point \((3,7)\), move 3 units to the right along the \(x\) - axis and 7 units up along the \(y\) - axis. Since the line is parallel to the \(x\) - axis, it is a horizontal line.

Part (b)

For a line parallel to the \(x\) - axis (horizontal line), the \(y\) - coordinate of every point on the line is the same. If the line passes through \((3,7)\), then another point on the line can be \((0,7)\) (or any other point where \(y = 7\) and \(x\) is a real number).

Part (c)

The general equation of a line parallel to the \(x\) - axis is \(y = k\), where \(k\) is the \(y\) - coordinate of any point on the line. Since the line passes through \((3,7)\), \(k = 7\).

Answer:

• (a) Plot the point \((3,7)\) (3 units right on \(x\), 7 units up on \(y\)) and draw a horizontal line through it.
• (b) Another point could be \((0,7)\) (any point with \(y = 7\) is correct).
• (c) The equation of the line is \(y=7\).