To find the equation of the line in the form $y = mx + c$, we need to determine the slope ($m$) and the y-intercept ($c$) of the line.

Step 1: Determine the slope ($m$)

The slope of the line is calculated using two known points on the line. Looking at the graph, we can extract two points:

• Point 1: $(-60, -120)$
• Point 2: $(0, -40)$

The formula for slope is:

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

Substitute the coordinates:

$m = \frac{-40 - (-120)}{0 - (-60)} = \frac{-40 + 120}{60} = \frac{80}{60} = \frac{4}{3}$

So, the slope $m = \frac{4}{3}$.

Step 2: Determine the y-intercept ($c$)

The y-intercept ($c$) is where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at $y = -40$, so $c = -40$.

Final equation of the line:

Now that we have $m = \frac{4}{3}$ and $c = -40$, the equation of the line is:

$y = \frac{4}{3}x - 40$

Would you like more details on any step or have any other questions?

Here are 5 related questions:

1. How can you find the slope of a line if only given the graph?
2. How does changing the slope ($m$) affect the appearance of a line?
3. What is the significance of the y-intercept in a linear equation?
4. How can you determine if two lines are parallel by looking at their equations?
5. What is the effect of changing the y-intercept ($c$) on the graph of a line?

Tip: The slope ($m$) tells us how steep the line is; a larger slope means a steeper line, while the sign of the slope indicates whether the line goes up or down as $x$ increases.