3a) Equation of a line formula: y - y₁ = m(x - x₁) x₁ and y₁ are coordinates of one point on the line m is the gradient of the line m = Δy/Δx = (y₂ - y₁)/(x₂ - x₁) If we say: (x₁, y₁) = (0, -1) (x₂, y₂) = (2, 3) then: m = (3 - -1)/(2 - 0) = 4/2 = 2 So, the equation of the line is (using the formula): y - -1 = 2(x - 0) y + 1 = 2x y = 2x - 1
3b) Any two given lines will always intersect unless they have the same gradient, i.e. they are parallel; So, to determine if the two lines will intersect all we have to do is work out the gradient of the second line and see if it is the same as the the gradient of the first (which we worked out to be 2) or not; So, for the second line: (x₁, y₁) = (-3, 3) (x₂, y₂) = (-2, 4) And so: m = (4 - 3)/(-2 - -3) = 1/1 = 1 1 ≠ 2; The gradients of the two lines are not the same; They are not parallel; They will intersect at some point.
4a) || Male || Female 0 ≤ x ≤ 1 || 66 || 2 2 ≤ x ≤ 7 || 583 || 160 8 ≤ x || 89 || 42 Total 738 204 x = number of times a day hand are washed
4b) 66/738 × 100 = 8.94..... ⇒ 9% 9% of males wash their hands once or less per day 2/204 × 100 = 0.980..... ⇒ 1% 1% of females wash their hands once or less per day
89/738 × 100 = 12.0..... ⇒ 12% 12% of males wash their hands 8 or more times per day 42/204 × 100 = 20.5..... ⇒ 21% 21% of females wash their hands 8 or more times per day
On average, it appears that females tend to wash their hands more frequently; However, the fact that significantly less women reported could mean the data is not suitable to be used to compare the number of hand washes between males and females. <span />
