First find the slope between any two points:
\(\sf Slope=\frac{y_2-y_1}{x_2-x_1}\)
Where \(\sf (x_1,y_1),(x_2,y_2)\) are the two points
So calculating the slope:
\(\sf Slope=\frac{7-5}{2-1}=\frac{2}{1}=2\)
So the slope is \(\boxed{2}\)
And our equation will be in the format of \(\sf y=mx+b\)
where \(\sf m~ is~ the ~slope\) and \(\sf b ~is~the~y-intercept\)
So, now we have half of the equation:
\(\sf y= 2x+b\)
Now to calculate b, we can plug in a point \(\sf (x,y)\) and solve for b.
So
\(\sf y= 2x+b\)
Lets use the point
\(\sf (1,5) which ~is~in~the~form ~of ~(x,y)\)
So:
\(\sf 5=2(1)+b\)
And then:
\(\sf b=3\)
So our final equation is \(\sf \boxed{y=2x+3}\)
