We are asked to find the equation of a line. Let's remember the general form of a line equation:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept. We are told that the line has a slope of 5, replacing that into the equation we get:
[tex]y=5x+b[/tex]Now, we are also told that the line passes through the point (-6,-7), which means that when x = -6, y = -7. We can use this to find "b", replacing in the equation, like this:
[tex]\begin{gathered} y=5x+b \\ -7=5(-6)+b \end{gathered}[/tex]Solving the operations:
[tex]-7=-30+b[/tex]Now we solve for "b", first by adding 30 on both sides:
[tex]\begin{gathered} -7+30=-30+30+b \\ 23=b \end{gathered}[/tex]Replacing the value of "b" into the equation of the line:
[tex]y=5x+23[/tex]And this is the equation of the line
