To determine the equation of the line shown in the graph, you need to follow these steps:

1. Find the slope ($m$):

   • Pick two points on the line from the graph (e.g., $(2, 0)$ and $(4, 4)$).
   • Use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ For the chosen points, $(x_1, y_1) = (2, 0)$ and $(x_2, y_2) = (4, 4)$: $m = \frac{4 - 0}{4 - 2} = \frac{4}{2} = 2$

2. Use the point-slope form of a line:

   • The general equation is: $y - y_1 = m(x - x_1)$ Substituting $m = 2$ and one of the points, e.g., $(2, 0)$: $y - 0 = 2(x - 2)$ Simplify: $y = 2x - 4$

3. Write the equation in slope-intercept form ($y = mx + b$):

   • The equation is already simplified to $y = 2x - 4$.

Final Answer:

The equation of the line is: $y = 2x - 4$

Do you need further explanation or additional examples?

Related Questions:

1. What is the slope of a line parallel to the one above?
2. How do you find the y-intercept of a line if the slope and a point are given?
3. How do you write the equation of a line perpendicular to the given line?
4. What changes in the graph when the slope is negative?
5. How would the equation change if the line passed through $(4, 8)$ instead?

Tip:

Always ensure you accurately pick points directly on the grid to avoid errors when calculating the slope.