The task is to write the equation of the line shown on the graph in terms of $x$. Let’s work through this step by step:

Step 1: Find the slope ($m$) of the line

To determine the slope, we use the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ From the graph:

• Choose two clear points on the line. For example:
  • Point 1: $(-3, -3)$
  • Point 2: $(3, 3)$

Substitute these into the formula: $m = \frac{3 - (-3)}{3 - (-3)} = \frac{6}{6} = 1$ So, the slope of the line is $m = 1$.

Step 2: Use the slope-intercept form ($y = mx + b$)

The slope-intercept form of a line is: $y = mx + b$ Now substitute $m = 1$: $y = x + b$

Step 3: Find the $y$-intercept ($b$)

The $y$-intercept is the point where the line crosses the $y$-axis ($x = 0$). From the graph, the line crosses the $y$-axis at $(0, 0)$. Thus, $b = 0$.

Final Equation:

Substitute $b = 0$ into the equation: $y = x$

Answer:

$\boxed{y = x}$

Would you like a detailed explanation of how to identify slope or intercept? Let me know if you have any further questions!

Related Questions:

1. How do you find the slope of a line from a graph?
2. What is the general form of a linear equation?
3. How do you determine the $y$-intercept from a graph?
4. Can the slope of a line be negative? How does it affect the graph?
5. How would the equation change if the line were parallel to this one but passed through a different point?

Tip:

Always double-check your chosen points for slope calculation to avoid errors!