Final answer:
The equation for the line in point-slope form that passes through the points (4,3) and (5,1) is y = -2x + 11. By finding the slope of -2 and using one of the given points, we can apply the point-slope formula to derive the equation.
Step-by-step explanation:
The objective is to write an equation in point-slope form for the line that passes through the points (4,3) and (5,1). To derive the equation, we first need to calculate the slope of the line, which is given by the formula:
slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Plugging in the given points:
m = (1 - 3) / (5 - 4)
m = (-2) / (1)
m = -2
Now that we have the slope, we can use the point-slope formula to write the equation:
y - y1 = m(x - x1)
Using the slope we calculated and one of the given points, for example, (4,3):
y - 3 = -2(x - 4)
y - 3 = -2x + 8
Finally, adding 3 to both sides to solve for y:
y = -2x + 11
The correct equation for the line in point-slope form that passes through the points (4,3) and (5,1) is y = -2x + 11, which corresponds to option a).