3. urgent
a. determine the equation of the line connecting the points (0,−1) and (2,3).

b. will the line described by the equation in part (a) intersect the line passing through the points (−2,4) and (−3,3)? explain why or why not.

4. students were asked to report their gender and how many times a day they typically wash their hands. of the 738 males, 66 said they wash their hands at most once a day, 583 said two to seven times per day, and 89 said eight or more times per day. of the 204 females, 2 said they wash their hands at most once a day, 160 said two to seven times per day, and 42 said eight or more times per day.

a. summarize these data in a two‐way table with rows corresponding to the
three different frequency‐of‐hand‐washing categories and columns corresponding to gender.

b. do these data suggest an association between gender and frequency of hand washing? support your answer with appropriate calculations.

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.