Answer:
y = 6x - 23
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points P(4, 1) and Q(3, -5). Substitute:
[tex]m=\dfrac{-5-1}{3-4}=\dfrac{-6}{-1}=6[/tex]
The refore we have the equation:
[tex]y=6x+b[/tex]
Put the coordinates of the point P(4, 1) to the equation:
[tex]1=6(4)+b[/tex]
[tex]1=24+b[/tex] subtract 24 from both sides
[tex]-23=b\to b=-23[/tex]
Finally we have the equation:
[tex]y=6x-23[/tex]
