Question

Find a point-slope form for the line with slope 5/1 and passing through the point (-6,-7).

Answer 1

We are asked to find the equation of a line. Let's remember the general form of a line equation:

`y=mx+b`

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:

`y=5x+b`

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:

`\begin{gathered} y=5x+b \\ -7=5(-6)+b \end{gathered}`

Solving the operations:

`-7=-30+b`

Now we solve for "b", first by adding 30 on both sides:

`\begin{gathered} -7+30=-30+30+b \\ 23=b \end{gathered}`

Replacing the value of "b" into the equation of the line:

`y=5x+23`

And this is the equation of the line