Question

graph the line $y = 5$.

Explanation:

Step1: Understand the equation

The equation \( y = 5 \) represents a horizontal line. For any value of \( x \), the \( y \)-coordinate is always 5. This is because in the slope - intercept form \( y=mx + b\) (where \( m \) is the slope and \( b \) is the y - intercept), for \( y = 5\), the slope \( m = 0\) (since there is no \( x \) term) and the y - intercept \( b=5\). A line with a slope of 0 is a horizontal line that passes through the point on the y - axis where \( y = 5\).

Step2: Identify points on the line

We can choose any \( x \)-values, and the corresponding \( y \)-value will be 5. For example, when \( x = 0\), \( y=5\) (the y - intercept point \((0,5)\)); when \( x = 1\), \( y = 5\) (the point \((1,5)\)); when \( x=- 1\), \( y = 5\) (the point \((- 1,5)\)).

Step3: Graph the line

On the given coordinate grid, find the horizontal line that passes through all points where the \( y \)-coordinate is 5. This line will be parallel to the \( x \)-axis and will pass through the \( y \)-axis at \( (0,5) \) and through other points like \( (1,5) \), \( (-1,5) \), \( (2,5) \), \( (-2,5) \) etc.

(Note: Since this is a graphing problem, the final answer is the graph of the horizontal line \( y = 5 \) on the provided coordinate plane. If we were to describe the key feature, the line is horizontal, passes through \( y = 5\) for all \( x \).)

Answer:

The line \( y = 5 \) is a horizontal line parallel to the \( x \) - axis, passing through all points with \( y \) - coordinate 5 (e.g., \((0,5)\), \((1,5)\), \((- 1,5)\) etc.) on the coordinate grid. To graph it, draw a straight horizontal line that intersects the \( y \) - axis at \( (0,5) \) and extends infinitely in both the positive and negative \( x \) - directions, maintaining a constant \( y \) - value of 5.