Question

what are the equations for lines l and m graphed below?
equation for line l:
equation for line m:

Explanation:

Step1: Analyze Line \( l \)

Line \( l \) passes through the origin \((0,0)\) and has a slope. Let's find two points on line \( l \). From the graph, when \( x = 0 \), \( y = 0 \); when \( x = 2 \), \( y=-2\) (assuming grid units). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 0}{2 - 0}=-1\). Using the slope - intercept form \( y = mx + b \), and \( b = 0 \) (since it passes through the origin), the equation of line \( l \) is \( y=-x \) (or \( y=-1x+0\)). Wait, maybe better to check the axes. Wait, the \( x \)-axis and \( y \)-axis: Wait, looking at the graph, line \( l \) seems to have a slope of \( 1 \) or \( - 1 \)? Wait, maybe I misread the axes. Wait, the \( y \)-axis is labeled \( y \), \( x \)-axis? Wait, the line \( l \): let's see, when \( x = - 2 \), \( y = 0 \); when \( x = 0 \), \( y=-2 \)? No, maybe the axes are \( x \) (horizontal) and \( y \) (vertical). Wait, line \( l \): let's take two points. If we consider the grid, maybe line \( l \) has a slope of \( 1 \)? Wait, no, maybe the line \( l \) is \( y=x \)? Wait, no, maybe I made a mistake. Wait, another approach: vertical and horizontal lines? No, line \( l \) is a diagonal line. Wait, maybe the line \( l \) passes through \((0,0)\) and \((2, - 2)\), so slope \( m=\frac{-2}{2}=-1\), so equation \( y=-x \).

Step2: Analyze Line \( m \)

Line \( m \) is a horizontal line. A horizontal line has a slope of \( 0 \), and its equation is of the form \( y = k \), where \( k \) is the \( y \)-coordinate of any point on the line. From the graph, line \( m \) passes through \( y = 4 \) (assuming the grid, looking at the \( y \)-axis, the horizontal line \( m \) is at \( y = 4 \)? Wait, no, wait the \( m \)-axis? Wait, the line \( m \) is horizontal, so its equation is \( y = 4 \)? Wait, no, maybe the \( y \)-coordinate for line \( m \) is \( 4 \)? Wait, looking at the graph, line \( m \) is a horizontal line, so \( y=\) constant. Let's see, the horizontal line \( m \): if we look at the \( y \)-axis, the line \( m \) is at \( y = 4 \)? Wait, maybe I misread. Wait, the line \( m \) is horizontal, so its equation is \( y = 4 \)? Wait, no, maybe the \( y \)-coordinate is \( 4 \). Wait, alternatively, maybe line \( m \) is \( y = 4 \) and line \( l \) is \( y=-x \). Wait, maybe the correct equations:

Wait, let's re - examine the graph. Line \( l \): passes through the origin and has a slope of \( 1 \) or \( - 1 \). Wait, if we take two points on line \( l \): when \( x = 0 \), \( y = 0 \); when \( x = 2 \), \( y=-2\), so slope \( m=-1\), equation \( y=-x \). Line \( m \): it's a horizontal line, so \( y = 4 \) (assuming the \( y \)-value where the horizontal line is). Wait, maybe the line \( m \) is \( y = 4 \) and line \( l \) is \( y=-x \).

Wait, maybe the correct equations:

For line \( l \): Let's assume the standard \( y = mx + b \). If the line passes through \((0,0)\) and \((2,-2)\), then \( m=\frac{-2 - 0}{2 - 0}=-1\), \( b = 0 \), so \( y=-x \).

For line \( m \): It's a horizontal line, so \( y = 4 \) (since it's parallel to the \( x \)-axis and passes through \( y = 4 \) on the \( y \)-axis).

Answer:

Equation for line \( l \): \( y=-x \) (or \( y = - 1x+0\))
Equation for line \( m \): \( y = 4 \)

(Note: The answer may vary slightly depending on the exact grid interpretation, but the general form for a horizontal line is \( y = k \) and for the diagonal line through the origin with slope - 1 is \( y=-x\))