The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - the point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (5, 4) and (2, -2). Substitute:
[tex]m=\dfrac{-2-4}{2-5}=\dfrac{-6}{-3}=2[/tex]
[tex]y-4=2(x-5)[/tex] - point-slope form
[tex]y-4=2x-10[/tex] add 4 to both sides
[tex]y=2x-6[/tex] - slope-intercept form
[tex]y=2x-6[/tex] subtract 2x from both sides
[tex]-2x+y=-6[/tex] change the signs
[tex]2x-y=6[/tex] - standard form
-------------------------------------------------------------------
From the table we have two points (1, 3) and (2, 7). SubstituteL
[tex]m=\dfrac{7-3}{2-1}=\dfrac{4}{1}=4[/tex]
[tex]y-3=4(x-1)[/tex] - point-slope form
[tex]y-3=4x-4[/tex] add 3 to both sides
[tex]y=4x-1[/tex] - slope-intercept form
[tex]y=4x-1[/tex] subtract 4x from both sides
[tex]-4x+y=-1[/tex] change the signs
[tex]4x-y=1[/tex] - standard form
