The linear function that passes through the point (3, 2) and creates a system of equations with the line below that has no solutions is given by:
[tex]y = -2x + 7[/tex]
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
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.
In this problem, it creates a system without solutions with the equation:
[tex]10x + 5y = 15[/tex]
[tex]5y = 15 - 10x[/tex]
[tex]y = -2x + 3[/tex]
That is, it has the same slope of m = -2, then:
[tex]y = -2x + b[/tex]
Since it passes through the point (3,2), we have that:
[tex]3 = -2 \times 2 + b[/tex]
[tex]b = 7[/tex]
Hence, the equation is:
[tex]y = -2x + 7[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
