Mathematics

# Write the equation For a Line that intersects points(1,3) And (2,5) which one is a.y=x+2 B.y=2x+1. C.y=3x-3. D.Y=-x+3 For me is letter B.please help

$3=a\cdot1+b\\ 5=a\cdot2+b\\\\ b=3-a\\ 2a+b=5\\\\ 2a+3-a=5\\ a=2\\\\ b=3-2\\ b=1\\\\ y=2x+1 \Rightarrow B$
$(1,3) ,\ \ (2,5) \\ \\ \\ First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} } \\ \\m=\frac{5-3}{2-1} = \frac{2}{1}=2 \\ \\Now \ use \ y = mx + b \ with \ either \ point \ to \ find \ b, \ the \ y-intercept \ : \\ \\ y=mx+b \\ \\3=2 \cdot 1+b\\ \\3= 2 +b \\ \\b=3-2=1 \\ \\ y=2x+1 \ is \ the \ answer \ B$