The slope-intercept form:
[tex]y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
m - slope
b - y-intercept
We have the points (1, -5) and (9, 11). Substitute:
[tex]m=\dfrac{11-(-5)}{9-1}=\dfrac{16}{8}=2[/tex]
Therefore we have
[tex]y=2x+b[/tex]
Put the coordinates of the point (1, -5) to the equation:
[tex]-5=2(1)+b\\\\-5=2+b\qquad\text{subtract 2 from both sides}\\\\-7=b\to b=-7[/tex]
Answer: y = 2x - 7
