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

1. Determine the slope $m$: The slope of a line is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

   From the graph, we can select two points on the line:

   • Point 1: $(0, 4)$ (This is where the line crosses the y-axis, which is also the y-intercept.)
   • Point 2: $(6, 1)$.

   Using the slope formula: $m = \frac{1 - 4}{6 - 0} = \frac{-3}{6} = -\frac{1}{2}$

2. Determine the y-intercept $b$: The y-intercept is the value of $y$ when $x = 0$. From the graph, we can see that the line crosses the y-axis at $y = 4$. Therefore, $b = 4$.

3. Write the equation: Substituting the slope $m = -\frac{1}{2}$ and y-intercept $b = 4$ into the slope-intercept form equation: $y = -\frac{1}{2}x + 4$

Thus, the equation of the line is $y = -\frac{1}{2}x + 4$.

Would you like more details or have any questions?

Related questions:

1. How do you find the slope of a line if only the graph is given?
2. What does the slope represent in real-world contexts?
3. How can you verify if a point lies on the line using the equation?
4. What changes to the equation occur if the slope is positive instead of negative?
5. How do you convert a line equation from standard form to slope-intercept form?

Tip:

When calculating the slope, make sure to pick two clear points on the line to avoid errors in reading the coordinates.