Mathematics
The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.
Straight Line Eq
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Answer
(i) Slope of the line PQ = tan 45° = 1.
(ii) Equation of line PQ can be given by point slope form i.e.,
⇒ y - y1 = m(x - x1)
⇒ y - 3 = 1(x - 5)
⇒ y - 3 = x - 5
⇒ x - y - 5 + 3 = 0
⇒ x - y - 2 = 0.
Hence, the equation of the line PQ is x - y - 2 = 0.
(iii) The line touches y-axis at Q there x-coordinate will be 0 so putting x = 0 in equation of line,
⇒ 0 - y - 2 = 0
⇒ y = -2.
Hence, coordinates of Q are (0, -2).
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