Given the point (5, 7) and the slope 2, using the point-slope form we have the equation of the line:
[tex]y-y_0=m(x-x_0)[/tex]Where m is the slope and x₀ and y₀ are the coordinates of the given point. From this problem, we identify m = 2, x₀ = 5, and y₀ = 7. Then:
[tex]y-7=2(x-5)\ldots(1)[/tex]The slope-intercept form is given by:
[tex]y=m\cdot x+b[/tex]Where m is the slope and b is the y-intercept. Using equation (1):
[tex]\begin{gathered} y=2x-10+7 \\ y=2x-3 \end{gathered}[/tex]