Tell whether the data in the table can be modeled by a linear equation.
X: 0, 1, 2, 4, 5
Y: 1.2, 1.4, 1.6, 2, 2.2
If possible, write a linear equation that represents y as a function of x
Yes, the data in the table can be modeled by a linear equation.
To find the linear equation that represents y as a function of x, we can find the slope of the line using two points from the table and then use the point-slope form of a linear equation.
Let's take the points (0, 1.2) and (5, 2.2). The slope can be calculated as:
slope = (change in y)/(change in x) = (2.2 - 1.2)/(5 - 0) = 1/5 = 0.2
Now, we can use the point-slope form of a linear equation with the point (0, 1.2):
y - y1 = m(x - x1)
Where y1 = 1.2 and x1 = 0:
y - 1.2 = 0.2(x - 0)
Simplifying:
y - 1.2 = 0.2x
Therefore, the linear equation that represents y as a function of x is:
y = 0.2x + 1.2