Mathematics
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.
Straight Line Eq
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Answer
(i) Gradient of a line =
Putting values in above formula we get,
Hence, the gradient of EF is 1.
(ii) Equation of EF can be given by,
y - y1 = m(x - x1)
Putting values in above equation we get,
⇒ y - 4 = 1(x - 0)
⇒ y - 4 = x
⇒ x - y + 4 = 0.
Hence, the equation of EF is x - y + 4 = 0.
(iii) The coordinates where EF intersects x-axis will be where y = 0.
Substituting y = 0 in x - y + 4 = 0 ,
⇒ x - 0 + 4 = 0
⇒ x = -4.
Hence, coordinates where EF intersects x-axis are (-4, 0).
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