Question

graph these equations:
$y = -x$
$y = 4$
click to select points on the graph.

Explanation:

Step1: Analyze \( y = -x \)

This is a linear equation with slope \( -1 \) and y - intercept \( 0 \). To graph it, we can find two points. When \( x = 0 \), \( y=0 \) (the origin \((0,0)\)). When \( x = 4 \), \( y=- 4\)? Wait, no, in the given graph, we see a point at \((0,4)\) and \((4,0)\) for the line \( y=-x + 4\)? Wait, no, the equation is \( y=-x \). Wait, maybe there was a miscalculation. Wait, the line in the graph passes through \((0,4)\) and \((4,0)\), which would be \( y=-x + 4\), but the given equation is \( y=-x \). Wait, maybe the user made a typo, but according to the given equation \( y=-x \), when \( x = 0 \), \( y = 0\); when \( x=1 \), \( y=-1\); when \( x=-1 \), \( y = 1\).

Step2: Analyze \( y = 4 \)

This is a horizontal line. For any value of \( x \), \( y = 4\). So we can plot points like \((0,4)\), \((1,4)\), \((-1,4)\) etc.

To graph \( y=-x \):

• Plot the point \((0,0)\) (since when \( x = 0 \), \( y = 0\)).
• Use the slope \( -1 \) (rise over run, so for a run of \( 1 \) (increase \( x \) by \( 1 \)), the rise is \( - 1 \) (decrease \( y \) by \( 1 \))). So from \((0,0)\), moving to \( (1,-1) \), \( (2,-2) \) etc.

To graph \( y = 4 \):

• Draw a horizontal line passing through all points with \( y \)-coordinate \( 4 \), like \((0,4)\), \((1,4)\), \((-1,4)\) etc.

(Note: The existing line in the graph seems to be \( y=-x + 4\) instead of \( y=-x \), but following the given equation \( y=-x \))

Answer:

To graph \( y=-x \): Plot points such as \((0,0)\), \((1, - 1)\), \((-1,1)\) and draw a line through them. To graph \( y = 4\): Draw a horizontal line through \((0,4)\), \((1,4)\), \((-1,4)\) etc. (If we consider the graph provided, there might be a discrepancy between the equation \( y=-x \) and the drawn line, but following the given equations, the above steps are for graphing \( y=-x \) and \( y = 4\))