Question

1. a line is graphed on a coordinate grid.

which statement about the line is true?
the equation of the line is x = 2, and the slope is undefined.
the equation of the line is y = 2, and the slope is equal to zero.
the equation of the line is x = 2, and the slope is equal to zero.
the equation of the line is y = 2, and the slope is undefined.
clear all

Explanation:

Step1: Analyze the graph

The line in the graph is horizontal, passing through \( y = 2 \) (since it intersects the y - axis at \( y = 2 \) and is parallel to the x - axis).

Step2: Recall slope and equation rules

• For a horizontal line, the equation is of the form \( y = k \) (where \( k \) is a constant), and the slope \( m=\frac{\Delta y}{\Delta x}\). Since \( \Delta y = 0 \) (change in y - value is zero for a horizontal line) and \( \Delta x

eq0 \), the slope \( m = 0 \).

• For a vertical line, the equation is of the form \( x = k \) and the slope is undefined (because \( \Delta x=0 \) and we cannot divide by zero).

Now let's analyze each option:

• Option 1: Says equation is \( x = 2 \) (vertical line) and slope undefined, but the graph is horizontal, so this is wrong.
• Option 2: Says equation is \( y = 2 \) (horizontal line) and slope is zero. This matches our analysis.
• Option 3: Says equation is \( x = 2 \) (vertical line) and slope zero, which is wrong because vertical lines have undefined slope.
• Option 4: Says equation is \( y = 2 \) (horizontal line) and slope undefined, which is wrong because horizontal lines have slope zero.

Answer:

The option: "The equation of the line is \( y = 2 \), and the slope is equal to zero." (the second option in the list)