Maths · Straight line: Various forms of equations of a line, intersection of lines, angles between two lines
What is the value of if ,(-5,6) \) and (-8,8) are collinear?
What is the value of \( y \) if \( (y, 3),(-5,6) \) and (-8,8) are collinear?
- A. -1
- B. 2
- C. \( \frac{1}{2} \)
- D. \( -\frac{1}{2} \)
Step-by-step solution
For collinearity, slopes between any two points are equal. Slope between (-5,6) and (-8,8) is (8-6)/(-8+5)=2/(-3)=-2/3. Slope between (y,3) and (-5,6) is (6-3)/(-5-y)=3/(-5-y). Set equal: 3/(-5-y) = -2/3. Cross multiply: 9 = 2(5+y) → 9 = 10+2y → 2y = -1 → y = -1/2.
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