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Question
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.
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).
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