Maths · Straight line: Various forms of equations of a line, intersection of lines, angles between two lines
Which of the following is/are true regarding the following linear equation: \)
Which of the following is/are true regarding the following linear equation: \( \boldsymbol{x}-\mathbf{3}=\frac{\mathbf{2}}{\mathbf{5}}(\boldsymbol{y}+\mathbf{1}) \)
- A. It passes through (0,-2.5) and \( m=-8.5 \)
- B. It passes through (0,-2.5) and \( m=8.5 \)
- C. It passes through (0,8.5) and \( m=-2.5 \)
- D. It passes through (0,-8.5) and \( m=2.5 \)
Step-by-step solution
Rewrite x - 3 = (2/5)(y + 1) in slope-intercept form: multiply both sides by 5 to get 5x - 15 = 2y + 2, then 2y = 5x - 17, so y = (5/2)x - 17/2. Hence slope m = 5/2 = 2.5 and y-intercept = -17/2 = -8.5, so the line passes through (0, -8.5).
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