A line passes through (–7, –5) and (–5, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.

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Answer:

[tex]\large\boxed{y-4=\dfrac{9}{2}(x+5)}\\\boxed{9x-2y=-53}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-7, -5) and (-5, 4).

Calculate the slope:

[tex]m=\dfrac{4-(-5)}{-5-(-7)}=\dfrac{9}{2}[/tex]

Put it and coordinates of the point (-5, 4) to the equation:

[tex]y-4=\dfrac{9}{2}(x-(-5))[/tex]

[tex]y-4=\dfrac{9}{2}(x+5)[/tex] → the point-slope form

Convert to the standard form Ax + By = C :

[tex]y-4=\dfrac{9}{2}(x+5)[/tex]         multiply both sides by 2

[tex]2y-8=9(x+5)[/tex]        use the distributive property

[tex]2y-8=9x+45[/tex]           add 8 to both sides

[tex]2y=9x+53[/tex]          subtract 9x from both sides

[tex]-9x+2y=53[/tex]           change the signs

[tex]9x-2y=-53[/tex] → the standard form

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