Answer:
[tex]\huge\boxed{y=2x-2}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁; y₁); (x₂; y₂) - points on a line
From the table we have
[tex](1,\ 0)\to x_1=1;\ y_1=0\\\\(2,\ 2)\to\ x_2=2;\ y_2=2[/tex]
Substitute:
[tex]m=\dfrac{2-0}{2-1}=\dfrac{2}{1}=2[/tex]
Put the value of a slope and coordinates of the point (1, 0) to the equation of a line:
[tex]0=2(1)+b[/tex]
[tex]0=2+b[/tex] subtract 2 from both sides
[tex]-2=b\to b=-2[/tex]
Finally we have:
[tex]y=2x-2[/tex]
