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# The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find: (i) The gradient of EF (ii) The equation of EF (iii) The coordinates of the point where the line EF intersects the x-axis.

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ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10
In this question coordinates of two points E and F are given (0, 4) and (3, 7)
Here, You have to find The gradient of EF ,the equation of EF and the coordinates of the point where the line EF intersects the x-axis.
This is the Question Number 17, Exercise 12.1 of M.L Aggarwal.

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1. Given, co-ordinates of points E and F are (0, 4) and (3, 7) respectively

m = y2Â â€“ y1Â / x2Â â€“ x1Â = (7 â€“ 4)/(3 â€“ 0) = 3/3

â‡’ m = 1

(ii) Equation of line EF is given by,

y â€“ y1Â = m (x â€“ x1)

y â€“ 7 = 1 (x â€“ 3)

y â€“ 7 = x â€“ 3

x â€“ y + 7 â€“ 3 = 0

Hence, the equation of line EF is x â€“ y + 4 = 0

(iii) Itâ€™s seen that the co-ordinates of point of intersection of EF and the x-axis will be y = 0

So, substituting the value y = 0 in the above equation

x â€“ y + 4 = 0

x â€“ 0 + 4 = 0

x = -4

Hence, the co-ordinates are (-4, 0).

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