To write the equation of the line in slope-intercept form ($y = mx + b$), let's calculate the slope ($m$) and y-intercept ($b$).

Step 1: Calculate the slope ($m$)

The slope formula is: $m = \frac{\text{rise}}{\text{run}}$ From the graph, two clear points on the line are: $(2, -6) \text{ and } (4, -2)$

The "rise" is the difference in the $y$-coordinates: $\text{rise} = -2 - (-6) = -2 + 6 = 4$

The "run" is the difference in the $x$-coordinates: $\text{run} = 4 - 2 = 2$

Thus, the slope is: $m = \frac{\text{rise}}{\text{run}} = \frac{4}{2} = 2$

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

The equation of the line is $y = mx + b$. Using $m = 2$, substitute one of the points into the equation to solve for $b$.

Using the point $(2, -6)$: $y = mx + b$ $-6 = 2(2) + b$ $-6 = 4 + b$ $b = -6 - 4 = -10$

Final Equation:

The slope-intercept form of the line is: $y = 2x - 10$

Would you like a breakdown of any specific step? Let me know if you have questions!

Related Questions:

1. How do you determine the slope if the graph is not clear?
2. Can the slope ever be negative, and what does it mean visually?
3. What is the point-slope form of this line?
4. How do you convert from slope-intercept form to standard form?
5. Why is the y-intercept useful in graphing a line?

Tip:

Always simplify the slope and ensure your answer is in the simplest form (integer or fraction).