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The line through P(5, 3) intersects y-axis at Q.

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. Equation of a Straight Line, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

(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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