Respuesta :
Answer:
[tex]y-1=\frac{1}{2}(x-10)[/tex]
Step-by-step explanation:
Let
x------>the time in minutes
y----> the number of people
we know that
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]A(10,1),B(18,5)[/tex]
Find the slope
[tex]m=\frac{5-1}{18-10}[/tex]
[tex]m=\frac{1}{2}\frac{people}{minutes}[/tex]
with the slope m and the point A find the equation of the line
[tex]y-1=\frac{1}{2}(x-10)[/tex] -----> point slope form
You can use the definition of slope of a line which is ratio of difference of dependent variable to the difference of independent variable.
The point slope form for the given condition is given by
[tex]y - 1 = \dfrac{x-10}{2}[/tex]
What is point slope form?
If the independent variable is denoted by symbol [tex]x[/tex] and the quantity(variable) depending on [tex]x[/tex] is denoted by [tex]y[/tex] symbol, and they have a linear relationship, then the point slope form for their relationship is given as
[tex]y -y_1= m(x-x_1)\\[/tex]
where m is the slope of the line representing their relation and [tex](x_1, y_1)[/tex] is coordinate of a point on that line.
(it is because each linear relationship between two variables can be represented by a straight line).
If two points are given on that line as [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
then slope of that line would be [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Thus, the point slope form will become
[tex]y -y_1= \dfrac{x_2 - y_1}{x_2 - x_1}(x-x_1)\\[/tex]
Since number of people is independent of how much time it takes to serve but time taken to serve is dependent on number of people, thus.
[tex]x = \text{Number of people = independent variable}\\y = \text{Time taken to serve = Dependent variable (depending on x)}[/tex]
Two data points given are:
[tex](x_1, y_1) = (1, 10)\\(x_2, y_2) = (5, 18)\\[/tex]
Thus, the point slope form for the given condition is given as
[tex]y -y_1= \dfrac{x_2 - y_1}{x_2 - x_1}(x-x_1)\\\\\\y - 1 = \dfrac{4}{8}(x-10) \\\\y - 1 = \dfrac{x-10}{2}[/tex]
Thus,
The point slope form for the given condition is given by
[tex]y - 1 = \dfrac{x-10}{2}[/tex]
Learn more about point slope form here:
https://brainly.com/question/11432370
