To complete the equation for the line shown in the graph, we need to determine two key values for the equation of a line, which has the form:

$y = mx + b$

where:

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

Step 1: Find the slope $m$

The slope is calculated as the change in $y$ divided by the change in $x$ between two points on the line:

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

Using the points $(1, 4)$ and $(0, 1)$ from the graph: $m = \frac{4 - 1}{1 - 0} = \frac{3}{1} = 3$

So, the slope $m = 3$.

Step 2: Find the y-intercept $b$

The y-intercept is the value of $y$ when $x = 0$. From the graph, the point $(0, 1)$ lies on the line, so the y-intercept $b = 1$.

Final Equation

Using the values of $m$ and $b$, the equation of the line is:

$y = 3x + 1$

Would you like further details or have any questions about the process?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the slope was negative?
2. What happens to the graph if the y-intercept $b$ changes?
3. Can you find the slope if the graph provided different points?
4. How do parallel lines relate to the slopes of linear equations?
5. What is the equation of a line with zero slope?

Tip: Always double-check the points you use to calculate slope to avoid errors!