A linear equation is represented as: [tex]y = mx + b[/tex].
The equation of the line is: [tex]y =3x - 14[/tex]
First, we calculate the slope (m) of [tex]6x + 18y = 11[/tex]
Make y the subject
[tex]18y = -6x + 11[/tex]
Divide by 18
[tex]y = -\frac{1}{3}x + \frac{11}{18}[/tex]
In [tex]y = mx + b[/tex]
[tex]m \to[/tex] slope
So, the slope of [tex]y = -\frac{1}{3}x + \frac{11}{18}[/tex] is:
[tex]m = -\frac 13[/tex]
Since, the line is perpendicular to [tex]6x + 18y = 11[/tex]
The slope of the line is:
[tex]m_1 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_1 = -\frac{1}{-1/3}[/tex]
[tex]m_1 = 3[/tex]
The line passes through (4,-2).
So, the equation is:
[tex]y =m(x - x_1) + y_1[/tex]
This gives:
[tex]y =3(x - 4) -2[/tex]
[tex]y =3x - 12 -2[/tex]
[tex]y =3x - 14[/tex]
Hence, the linear equation is:
[tex]y =3x - 14[/tex]
Read more about at:
https://brainly.com/question/11897796
