Answer:
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
Te formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
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We have two points: (2, -3) and (4, 2). Substitute:
[tex]m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]
[tex]y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)[/tex]
Convert it to the standard form [tex]Ax+By=C[/tex]:
[tex]y+3=\dfrac{5}{2}(x-2)[/tex] multiply both sides by 2
[tex]2y+6=5(x+2)[/tex] use the coordinates of the point
[tex]2y+6=5x+10[/tex] subtract 6 from both sides
[tex]2y=5x+4[/tex] subtract 5x from both sides
[tex]-5x+2y=4[/tex] change the signs
[tex]5x-2y=-4[/tex]
