To find the equation of the line shown in the graph, we need to determine its slope and y-intercept. The general equation for a line is:

$y = mx + b$

where:

• $m$ is the slope,
• $b$ is the y-intercept.

1. Identifying two points

From the graph, the line passes through two visible points:

• Point $A(0, 4)$, which is on the y-axis.
• Point $B(4, -4)$.

2. Calculating the slope ($m$)

The slope is given by:

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

Using the points $A(0, 4)$ and $B(4, -4)$:

• $x_1 = 0$, $y_1 = 4$
• $x_2 = 4$, $y_2 = -4$

Substitute into the formula:

$m = \frac{-4 - 4}{4 - 0} = \frac{-8}{4} = -2$

Thus, the slope $m$ is $-2$.

3. Finding the y-intercept ($b$)

The y-intercept is where $x = 0$. From point $A(0, 4)$, we see that $b = 4$.

4. Writing the equation

Substitute $m = -2$ and $b = 4$ into the general equation $y = mx + b$:

$y = -2x + 4$

Final Answer:

The equation of the line is:

$y = -2x + 4$

Let me know if you need further explanation or help plotting it step-by-step.

Related Questions:

1. How do you determine the slope if you are given two points?
2. What is the slope-intercept form of a linear equation?
3. How can you rewrite a linear equation in standard form?
4. How does the graph of a line change when the slope or intercept changes?
5. What is the significance of the y-intercept?

Tip: The slope tells you the steepness and direction of the line. A negative slope means the line is slanting downwards from left to right.