The problem asks to find a linear formula for the given line in the form $y = a \cdot x + b$, where $a$ is the slope and $b$ is the y-intercept.

Let's break down the process:

Step 1: Identify two points on the line

From the graph, it looks like two points are:

1. $(0, 90)$
2. $(100, 100)$

Step 2: Calculate the slope $a$

The slope $a$ is given by the formula: $a = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(0, 90)$ and $(100, 100)$ into the formula: $a = \frac{100 - 90}{100 - 0} = \frac{10}{100} = 0.1$

Step 3: Find the y-intercept $b$

The y-intercept is the value of $y$ when $x = 0$. From the point $(0, 90)$, we can directly see that $b = 90$.

Step 4: Write the equation

Now, substitute $a = 0.1$ and $b = 90$ into the equation $y = a \cdot x + b$: $y = 0.1x + 90$

This is the linear equation for the given line.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How can we verify that a point lies on a given line?
2. How does changing the slope $a$ affect the steepness of the line?
3. What happens to the graph if we change the y-intercept $b$?
4. How can you determine the slope from a graph with points that are not integers?
5. How would the equation change if the line had a negative slope?

Tip: When identifying the slope on a graph, always look for two points where the coordinates are easy to read (like integers).