To determine the rate of change (slope) and the initial value (y-intercept) of the linear function based on the graph:

Step 1: Calculate the rate of change (slope)

The slope $m$ is given by:

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

1. Identify two distinct points on the line from the graph, say $(x_1, y_1)$ and $(x_2, y_2)$.
2. Substitute their coordinates into the formula to calculate $m$.

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Step 2: Determine the initial value (y-intercept)

The y-intercept is the point where the line crosses the $y$-axis (i.e., $x = 0$).

• If the graph is not clear, substitute $m$ and one point into the slope-intercept form of the line:

$y = mx + b$

Solve for $b$, the y-intercept.

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Please share specific points or provide the graph to proceed further. This will allow accurate computation of the slope and initial value.

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Would you like assistance extracting points or understanding graph interpretation? 😊

Related Questions:

1. What is the significance of the rate of change in real-world scenarios?
2. How do you calculate the slope from a table instead of a graph?
3. Why is the y-intercept useful in understanding the function's context?
4. Can a linear function have a slope of zero? What would it look like?
5. How do horizontal and vertical lines differ in slope and y-intercept?

Tip:

Always double-check your chosen points to avoid calculation errors in finding the slope!