The equation of line R can be written in the form y = mx + c. What are the values o...

1. Identify the y-intercept (c): The y-intercept is the point where the line crosses the y-axis. On the graph, Line R crosses the y-axis at $y = -1$. Therefore, $c = -1$.
2. Identify two points on the line: To find the slope, we need two distinct points on the line. From the graph, we can identify the following points:
- Point 1: $(0, -1)$ (this is the y-intercept)
- Point 2: $(1, 2)$
- Point 3: $(2, 5)$
3. Calculate the slope (m): The slope of a line is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using Point 1 $(0, -1)$ and Point 2 $(1, 2)$:
$$m = \frac{2 - (-1)}{1 - 0} = \frac{2 + 1}{1} = \frac{3}{1} = 3$$
We can verify this using Point 2 $(1, 2)$ and Point 3 $(2, 5)$:
$$m = \frac{5 - 2}{2 - 1} = \frac{3}{1} = 3$$
The slope $m$ is 3.
4. Write the equation of the line: Now that we have the slope ($m=3$) and the y-intercept ($c=-1$), we can write the equation of the line in the form $y = mx + c$. Substituting the values, we get:
$$y = 3x + (-1)$$
$$y = 3x - 1$$