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ANSWER

The equation of the given line is

[tex]4y - 3x + 18 = 0[/tex]

EXPLANATION

The line passes through the points
[tex](2,-3) \: and \: ( - 2,-6)[/tex]

We can use these two points to determine the slope as follows:

[tex]slope = \frac{ - 6 - - 3}{ - 2 - 2} [/tex]

[tex]slope = \frac{ - 6 + 3}{ - 2 - 2} [/tex]

[tex]slope = \frac{ -3}{ - 4} = \frac{3}{4} [/tex]

We now apply the point slope formula

[tex]y-y_1=m(x-x_1)[/tex]

to obtain,

[tex]y + 3 = \frac{3}{4} (x - 2)[/tex]

We multiply through by 4 to get,

[tex]4y + 12 = 3(x - 2)[/tex]

This gives us,

[tex]4y + 12 = 3x - 6[/tex]

We simplify further to get,

[tex]4y - 3x + 18 = 0[/tex]

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