To find the equation of the line that passes through the points (1, 5) and (2, 14), we first need to determine the slope (m) of the line using the formula:
m = (y2 – y1) / (x2 – x1)
In our case, (x1, y1) is (1, 5) and (x2, y2) is (2, 14). Plugging in these values, we get:
m = (14 – 5) / (2 – 1) = 9 / 1 = 9
Now that we have the slope, we can use the slope-intercept form of a line, which is:
y = mx + b
Next, we need to find the y-intercept (b). We can use one of the points to help us with this. Let’s use the point (1, 5):
5 = 9(1) + b
Solving for b:
5 = 9 + b
b = 5 – 9 = -4
Now we can write the equation of the line:
y = 9x – 4
This is the equation of the line in slope-intercept form that passes through the points (1, 5) and (2, 14).