The graph in the image shows a straight line, and we are asked to write the equation of the line where $y$ depends on $x$.

To write the equation of a straight line, we use the slope-intercept form:

$y = mx + b$

Where:

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

Step 1: Identify the y-intercept ($b$)

From the graph, the line crosses the y-axis at $y = 7$, so:

$b = 7$

Step 2: Calculate the slope ($m$)

The slope $m$ is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

From the graph, two clear points are:

• $(0, 7)$ (the y-intercept)
• $(2, 4)$

The slope $m$ is calculated as follows:

$m = \frac{\text{rise}}{\text{run}} = \frac{4 - 7}{2 - 0} = \frac{-3}{2}$

Step 3: Write the equation

Now that we know the slope $m = -\frac{3}{2}$ and the y-intercept $b = 7$, the equation of the line is:

$y = -\frac{3}{2}x + 7$

Would you like further clarification, or do you have any questions?

Here are five related questions for practice:

1. What is the equation of a line with slope $\frac{1}{2}$ and y-intercept $3$?
2. If the line passes through points $(1, 4)$ and $(-1, 2)$, how do you find its equation?
3. How do you determine the slope of a line given its equation in standard form $Ax + By = C$?
4. What is the slope of a line parallel to $y = -\frac{3}{2}x + 7$?
5. How would the equation change if the line were shifted 3 units down?

Tip: When finding the slope, always carefully pick points where the line crosses grid intersections for more accurate calculations.