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