determine another point on the line given two points on the line. (0, 5), (4, 1) a) (1, 4) b) (2, 3) c) (1…
determine another point on the line given two points on the line. (0, 5), (4, 1) a) (1, 4) b) (2, 3) c) (1, 6) d) (4, 11)
Answer
Explanation:
Step1: Find the slope of the line
The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(0,5)) and ((x_2,y_2)=(4,1)). Then (m=\frac{1 - 5}{4-0}=\frac{-4}{4}=- 1).
Step2: Use the point - slope form (y - y_1=m(x - x_1))
Using the point ((0,5)) and (m=-1), the equation of the line is (y - 5=-1(x - 0)), which simplifies to (y=-x + 5).
Step3: Check each option
- For option A: When (x = 1), (y=-1+5 = 4).
- For option B: When (x = 2), (y=-2 + 5=3).
- For option C: When (x = 1), (y=-1+5 = 4\neq6).
- For option D: When (x = 4), (y=-4 + 5=1\neq11).
Answer:
B. ((2,3))