use the graph to derive the equation of the line in slope-intercept form.
To derive the equation of the line in slope-intercept form from the graph, we need to identify two points on the line and use them to calculate the slope and y-intercept.
In the given graph, two points that lie on the line are (1, 2) and (4, 5).
First, calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (5 - 2) / (4 - 1)
m = 3 / 3
m = 1
Now, we have the slope of the line, which is 1. Next, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
Now, substitute the slope m = 1 and the coordinates of one of the points (1, 2) into the equation to solve for the y-intercept (b).
2 = 1(1) + b
2 = 1 + b
b = 2 - 1
b = 1
Therefore, the equation of the line in slope-intercept form is:
y = x + 1.