Final answer:
To write the line's equation in point-slope form that passes through (2, 1) and (3, 5), calculate the slope as 4 and use one point: y - 1 = 4(x - 2).
Step-by-step explanation:
The question asks us to write the point-slope form of the line that passes through the points (2, 1) and (3, 5). To write the equation of a line in point-slope form, we first need to determine the slope of the line. We can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
By substituting the given points into the formula, we obtain:
m = (5 - 1) / (3 - 2) = 4 / 1 = 4
Now that we have the slope, we can use one of the points to write the equation in point-slope form, which is y - y1 = m(x - x1). Let's choose the point (2, 1).
The equation is:
y - 1 = 4(x - 2)
This represents the line in point-slope form with a slope of 4 that passes through the point (2, 1).