Answer:
[tex]y = 6x+19[/tex]
Step-by-step explanation:
Since we are given the slope and a point, we can using the point-slope form of a line and solve to get the slope-intercept form of the line.
Solving:
[tex]\subsection*{Point-Slope Form:}The point-slope form of the equation of a line is given by:\[y - y_1 = m(x - x_1)\][/tex]
[tex]\subsection*{Plug into Point-Slope:}Substituting \(m = 6\), \(x_1 = -2\), and \(y_1 = 7\):\[y - 7 = 6(x - (-2))\]\[y - 7 = 6(x + 2)\]Distributing the slope:\[y - 7 = 6x + 12\]Adding \(7\) to both sides:\[y = 6x + 12 + 7\]\[\boxed{y = 6x + 19}\][/tex]
Therefore, the equation of the line is y = 6x + 19.
