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The Line Through P(5, 3) Intersects Y-axis at Q. (1) Write the Slope of the Line. (2) Write the Equation of the Line. (3) Find the Co-ordinates of Q. - Mathematics

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

(1) Write the slope of the line.
(2) Write the equation of the line.
(3) Find the coordinates of Q.

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Solution

1) Since the line make 45o with the positive direction of x-axis,
Therefore slope (m) = tan 45° = 1

2) An equation of a line, using point-slope is

`y - y_1 = m(x - x_1)`

`=> y - 3 = 1 (x - 5)`

`=> y - 3 = x - 5`

`=>  y = x - 2`

3) Since Q is a point on y-axis, its x-coordinate is zero.

Putting x = 0 in the equation of line, we get y = –2

Hence the point Q is (0, –2).

Concept: Slope of a Line
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