Answer:
[tex]f(x) = x - 3[/tex]
Step-by-step explanation:
Linear equation form:
[tex]y=mx+b[/tex]
m is the slope
b is the y intercept
Solve for m using the first two points:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{6-7}{3-4}[/tex]
[tex]m=\frac{-1}{-1}[/tex]
[tex]m=1[/tex]
Plug in m and either point into the equation and solve for b:
[tex]y=mx+b[/tex]
[tex]4=1(7)+b[/tex]
[tex]4=7+b[/tex]
[tex]b=4-7[/tex]
[tex]b=-3[/tex]
Final equation:
[tex]y=x-3[/tex]
Test with the 3rd point:
[tex]2=5-3[/tex]
[tex]2=2[/tex]
Equation fits all 3 points
