Question

The graph of a linear function is shown on the grid.

Write an equation in slope-intercept form for this graph.

Answer 1

To write the equation of a linear function in slope-intercept form, which is \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), you need to determine both the slope and the y-intercept from the graph.

1. **Identify the y-intercept (b)**: This is the point where the line crosses the y-axis. Look at the graph to find this point. For example, if the line crosses at \( (0, 2) \), then \( b = 2 \).

2. **Calculate the slope (m)**: The slope is calculated as the rise over run between two points on the line. Choose two points on the line, for example, \( (x_1, y_1) \) and \( (x_2, y_2) \). The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plug in the coordinates of your chosen points to find the slope.

3. **Write the equation**: After determining the values for \(m\) (slope) and \(b\) (y-intercept), substitute these values into the slope-intercept form \(y = mx + b\) to get your final equation.

If you have specific points or the y-intercept from the graph, please provide them, and I can assist you in creating the exact equation!