To find the equation of the line passing through the points (1, 1) and (2, 4), we can use the slope-intercept form of a line equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to calculate the slope (m) using the formula:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (1, 1) and (x2, y2) = (2, 4). Plugging in these values gives us:
m = (4 – 1) / (2 – 1) = 3 / 1 = 3
Now that we have the slope, we can use one of the points to find the y-intercept (b). We’ll use the point (1, 1) for this. Substituting in the slope and the coordinates of the point into the slope-intercept equation:
1 = 3(1) + b
Simplifying this:
1 = 3 + b
b = 1 – 3 = -2
Now that we have both the slope and the y-intercept, we can write the equation of the line:
y = 3x – 2
This is the equation of the line that passes through the points (1, 1) and (2, 4).