To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).

Step 1: Identify two points on the line

From the graph:

• The line appears to pass through the points $(-6, -4)$ and $(6, 3)$.

Step 2: Calculate the slope (m)

The slope $m$ is calculated using the formula:

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

Substituting the points $(-6, -4)$ and $(6, 3)$ into the formula:

$m = \frac{3 - (-4)}{6 - (-6)} = \frac{3 + 4}{6 + 6} = \frac{7}{12}$

Step 3: Determine the y-intercept (b)

The slope-intercept form is:

$y = mx + b$

We can use one of the points to solve for $b$. Let's use the point $(6, 3)$:

$3 = \frac{7}{12} \times 6 + b$

$3 = \frac{7 \times 6}{12} + b = \frac{42}{12} + b = 3.5 + b$

$b = 3 - 3.5 = -0.5$

Step 4: Write the final equation

The equation of the line in slope-intercept form is:

$y = \frac{7}{12}x - \frac{1}{2}$

Would you like further details or have any questions?

Related Questions:

1. How do you calculate the slope between two points on a graph?
2. What is the significance of the y-intercept in the slope-intercept form of a line?
3. How can you determine the equation of a line if you only know its slope and a single point?
4. What is the difference between the slope-intercept form and the point-slope form of a line?
5. How do you convert an equation from standard form to slope-intercept form?

Tip: When identifying points on a graph, choose points where the line crosses grid intersections to ensure more accurate calculations.