Final answer:
To find the equation of the line in point-slope form that passes through (4,3) and (5,1), calculate the slope using the slope formula, then plug the slope and one point into the point-slope equation, which yields y - 3 = -2(x - 4).
Step-by-step explanation:
To write an equation for the line in point-slope form that passes through the points (4,3) and (5,1), we first need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
For the given points (4,3) and (5,1), we can substitute into the formula to find the slope:
m = (1 - 3) / (5 - 4) = -2 / 1 = -2
Once we have the slope, we can use either point to calculate the point-slope form of the equation. We'll use the point (4,3). The point-slope form of the equation is given by:
y - y1 = m(x - x1)
Plugging in the values gives us:
y - 3 = -2(x - 4)
This is the equation of the line in point-slope form that passes through the given points.