(2,1)
(4,2)
(5,2.5)
(30,15)
what is the slope in context
what is the y intercept in contex
what is the equation of the line?
To find the slope, we can use the formula:
slope = (change in y)/(change in x)
Using the given points:
slope = (2.5-1)/(5-4) = 1.5
The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope indicates that for every one unit increase in x, the corresponding y value increases by 1.5 units.
To find the y-intercept, we can use the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept.
Using one of the given points, such as (2,1):
1 = 2 * 1.5 + b
1 = 3 + b
Simplifying the equation, we find:
b = -2
The y-intercept represents the y-value when x is equal to zero. In this context, the y-intercept is -2.
Thus, the equation of the line is:
y = 1.5x - 2