Answer:
\(y=2x+3\)
Step-by-step explanation:
the general form of a line is:
\(y=mx+b\)
where m is the slope, and b is the point where the line crosses the y-axis.
From the graph we can see that said line crosses the y-axis at
+3
the the b in our solution must be+3 , we willl have a result of the form:
\(y=mx+3\)
That rules out options A and C
Now to calculate the slope we take two points where the graph passes, I will take the points:
\((-2,-1)and (0,3)\)
tag the coordinates
\(x_{1}=-2\\y_{1}=-1\\x_{2}=0\\y_{2}=3\)
and use the slope equation
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
substituting the values:
\(m=\frac{3-(-1)}{0-(-2)} \\m=\frac{3+1}{2}\\ m=\frac{4}{2} \\m=2\)
the slope of the line is 2, so the equation of the line is:
\(y=2x+3\)
which is option B
