Respuesta :
The linear equation that respects the given conditions is:
[tex]y = \frac{3}{2}x + [/tex]
What is a linear function?
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.
When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.
[tex]2x + 3y = 4[/tex]
[tex]3y = -2x + 4[/tex]
[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]
Then:
[tex]-\frac{2}{3}m = -1[/tex]
[tex]m = \frac{3}{2}[/tex]
Hence:
[tex]y = \frac{3}{2}x + b[/tex]
It passes through (−2, 15), that is, when x = -2, y = 15, hence:
[tex]y = \frac{3}{2}x + b[/tex]
[tex]15 = \frac{3}{2}(-2) + b[/tex]
15 = -3 + b
b = 18.
So the equation is:
[tex]y = \frac{3}{2}x + [/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
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