The problem asks us to find the values of $m$ and $c$ in the equation $y = mx + c$ for the given line R. $m$ represents the slope of the line, and $c$ represents the y-intercept.

1. Problem Description

The problem asks us to find the values of $m$ and $c$ in the equation $y = mx + c$ for the given line R. $m$ represents the slope of the line, and $c$ represents the y-intercept.

2. Solution Steps

First, we need to identify two points on the line from the graph. Two clear points are $(0, -4)$ and $(1, -1)$.

The y-intercept is the value of $y$ when $x = 0$. From the point $(0, -4)$, we can directly read off the y-intercept, which is $c = -4$.

Next, we calculate the slope $m$ using the two points $(x_1, y_1) = (0, -4)$ and $(x_2, y_2) = (1, -1)$.

The formula for the slope $m$ is:

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

Plugging in the coordinates:

$m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3$

Therefore, $m = 3$.

3. Final Answer

$m = 3$

$c = -4$