Question

1. which of the following is the graph of the equation below?

$y = -\frac{1}{5}x + 2$
(there are four graphs with options: option 1, option 2, and two other options with blue lines on coordinate grids)

Explanation:

Step1: Analyze the slope and y-intercept

The equation \( y = -\frac{1}{5}x + 2 \) is in slope - intercept form \( y=mx + b \), where \( m=-\frac{1}{5} \) (slope) and \( b = 2 \) (y - intercept). The slope is negative, so the line should be decreasing from left to right. The y - intercept is 2, so the line crosses the y - axis at \( (0,2) \).

Step2: Evaluate each option

• Option 1: The line has a steep negative slope (steeper than \( -\frac{1}{5} \)) and the y - intercept seems to be 2, but the slope magnitude is too large.
• Option 2: The line has a positive slope, which does not match \( m =-\frac{1}{5} \) (negative slope).
• The third option (lower left): The y - intercept is not 2 (it seems to be around 1 or 0), so it is incorrect.
• The fourth option (lower right): The line has a negative slope (decreasing from left to right), and the y - intercept is 2 (crosses the y - axis at \( (0,2) \)). Also, the slope is a small negative value (consistent with \( -\frac{1}{5} \)) as the line is not very steep.

Answer:

The graph on the lower right (the fourth graph)