Question

graph the line with the equation $y = -x + 5$.

Explanation:

Step1: Identify slope and y-intercept

The equation \( y = -x + 5 \) is in slope - intercept form \( y=mx + b \), where \( m=- 1 \) (slope) and \( b = 5 \) (y - intercept). So the line crosses the y - axis at \( (0,5) \).

Step2: Find another point using slope

The slope \( m=-1=\frac{-1}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move down 1 unit (decrease in \( y \) by 1). Starting from \( (0,5) \), if we move 1 unit right to \( x = 1 \), then \( y=5 - 1=4 \), so we get the point \( (1,4) \). We can also use the slope in the other direction: for every 1 unit left (decrease in \( x \) by 1), we move up 1 unit (increase in \( y \) by 1). From \( (0,5) \), moving left to \( x=-1 \), \( y = 5+1 = 6 \), giving the point \( (-1,6) \).

Step3: Plot the points and draw the line

Plot the points \( (0,5) \), \( (1,4) \), \( (-1,6) \) (or other points found using the slope) on the coordinate plane and then draw a straight line through them.

Answer:

To graph \( y=-x + 5 \):

1. Plot the y - intercept at \( (0,5) \) (since when \( x = 0 \), \( y=5 \)).
2. Use the slope \( m=-1 \) to find another point. For example, from \( (0,5) \), move 1 unit right and 1 unit down to get \( (1,4) \), or 1 unit left and 1 unit up to get \( (-1,6) \).
3. Draw a straight line through the plotted points.