The problem asks us to find the equation of line $l$ and line $m$ in slope-intercept form. The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Problem Description

The problem asks us to find the equation of line $l$ and line $m$ in slope-intercept form. The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Solution Steps

a. Find the equation of line $l$.

First, we need to find two points on the line $l$. From the graph, we can observe that the line passes through the points $(0,0)$ and $(4,4)$.

The slope $m$ is given by

$m = \frac{y_2 - y_1}{x_2 - x_1}$.

Using the points $(0,0)$ and $(4,4)$, we have

$m = \frac{4-0}{4-0} = \frac{4}{4} = 1$.

The y-intercept is the point where the line intersects the y-axis. From the graph, we can see that the line $l$ intersects the y-axis at the point $(0,0)$. Therefore, the y-intercept is $b=0$.

The equation of line $l$ in slope-intercept form is

$y = mx + b = 1x + 0 = x$.

Thus, $y = x$.

b. Find the equation of line $m$.

We need to find two points on the line $m$. From the graph, we can observe that the line passes through the points $(-4,4)$ and $(4,0)$.

The slope $m$ is given by

$m = \frac{y_2 - y_1}{x_2 - x_1}$.

Using the points $(-4,4)$ and $(4,0)$, we have

$m = \frac{0-4}{4-(-4)} = \frac{-4}{4+4} = \frac{-4}{8} = -\frac{1}{2}$.

The y-intercept is the point where the line intersects the y-axis. From the graph, we can see that the line $m$ intersects the y-axis at the point $(0,2)$. Therefore, the y-intercept is $b=2$.

The equation of line $m$ in slope-intercept form is

$y = mx + b = -\frac{1}{2}x + 2$.

3. Final Answer

a. The equation of line $l$ is $y=x$.

b. The equation of line $m$ is $y=-\frac{1}{2}x + 2$.