Question

find the slope and y - intercept of the line. graph the line.
y = -x
answer the following, and then choose the correct box to complete each item.
a. slope =
(open its image in a separate browser.)
b. the slope is undefined.
answer the following, and then choose the correct box to complete each item.
a. y - intercept =
(open its image in a separate browser.)
b. the line y = -x does not have a y - intercept.
use the graphing tool to graph the equation.
(click to
enlarge
graph)

Explanation:

Step1: Identify the function type

The function given is \( y = -x \), which is a linear function in the form \( y = mx + b \) where \( m=-1 \) (slope) and \( b = 0 \) (y - intercept).

Step2: Analyze the slope and y - intercept

• The slope \( m=-1 \) means that for every 1 unit we move to the right along the x - axis, we move down 1 unit along the y - axis.
• The y - intercept \( b = 0 \) means the line passes through the origin \((0,0)\).

Step3: Graph the function

To graph \( y=-x \), we can use the two - point method.

• When \( x = 0 \), \( y=-0 = 0 \), so we have the point \((0,0)\).
• When \( x = 1 \), \( y=-1 \), so we have the point \((1, - 1)\).
• When \( x=-1 \), \( y = -(-1)=1 \), so we have the point \((-1,1)\).
• Plot these points and draw a straight line through them. The line should have a negative slope (going from the top - left to the bottom - right) and pass through the origin.

Answer:

The graph of \( y = -x \) is a straight line with a slope of - 1 passing through the origin \((0,0)\). To plot it, use points like \((0,0)\), \((1, - 1)\) and \((-1,1)\) and draw a line through them.