The slope-intercept form of a line is given by the equation:

$y = mx + b$

where:

• $m$ is the slope of the line,
• $b$ is the y-intercept (the point where the line crosses the y-axis).

Step 1: Determine the slope ($m$)

The slope $m$ can be found by identifying two points on the line and using the formula:

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

Looking at the graph, we can choose two points:

• The line passes through the point $(0, 1)$, which is the y-intercept.
• It also passes through the point $(2, -1)$.

Using these points:

$m = \frac{-1 - 1}{2 - 0} = \frac{-2}{2} = -1$

So, the slope $m = -1$.

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

The line crosses the y-axis at $(0, 1)$, so the y-intercept $b = 1$.

Final Equation:

Substitute the values of $m$ and $b$ into the slope-intercept form:

$y = -x + 1$

This is the equation of the line.

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. What is the equation of a line with a slope of 2 and a y-intercept of -3?
2. How do you find the x-intercept of a line from its equation?
3. Can a line have an undefined slope? What does it represent?
4. How would the equation change if the slope was positive?
5. What is the general form of a linear equation?

Tip: When identifying points on a graph, it's useful to pick points where the line clearly crosses grid intersections for better accuracy.