To find the equation of the line graphed in the image, follow these steps:

Step 1: Identify two points on the line

From the graph, two points on the line are:

1. $(-3, 5)$
2. $(3, -3)$

Step 2: Calculate the slope ($m$)

The slope $m$ is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates of the points: $m = \frac{-3 - 5}{3 - (-3)} = \frac{-8}{6} = -\frac{4}{3}$

Step 3: Use the point-slope form of a line

The point-slope form is: $y - y_1 = m(x - x_1)$ Using point $(-3, 5)$ and $m = -\frac{4}{3}$, substitute: $y - 5 = -\frac{4}{3}(x + 3)$

Step 4: Simplify to slope-intercept form

Distribute and simplify: $y - 5 = -\frac{4}{3}x - 4$ $y = -\frac{4}{3}x + 1$

Final Answer:

The equation of the line is: $y = -\frac{4}{3}x + 1$

Let me know if you'd like additional clarification!

Relative Questions:

1. How do you convert between different forms of a linear equation (e.g., point-slope to standard form)?
2. Can a line have a slope of 0? What would the equation look like?
3. What is the difference between positive and negative slopes in terms of graph appearance?
4. How do you determine if two lines are parallel or perpendicular from their equations?
5. Can you find the equation of a line if only given one point and the slope?

Tip:

Always reduce the slope to its simplest fraction form for clarity and accuracy in equations.