Considering that the points are part of the same linear function, the missing x-value is given by:
a. 1.1.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
Given two points, the slope is given by <u>change in y divided by change in x</u>. In this problem, we are given points (6, 10.2) and (1.5, 3.45), hence the slope is:
m = (10.2 - 3.45)/(6 - 1.5) = 1.5.
Hence:
y = 1.5x + b.
When x = 6, y = 10.2, hence we use it to find b as follows:
10.2 = 1.5(6) + b
9 + b = 10.2
b = 1.2.
Hence the function is:
y = 1.5x + 1.2.
The value of x when y = 2.85 is given by:
y = 1.5x + 1.2.
2.85 = 1.5x + 1.2.
1.5x = 1.65.
x = 1.65/1.5
x = 1.1.
Hence option A is correct.
More can be learned about linear functions at brainly.com/question/24808124
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