Question

What is the equation of a line that passes through point (-1,5) and has the slope of m=4

Answer 1

The general equation of a line is given as;

`y=mx+b`

In this question, the slope (which is m) is given as 4. Also we have the points x and y, given as (-1, 5). That is;

`x=-1,y=5`

Therefore the next step is to find the y-intercept (that is b in the equation).

We substitute for the known values as follows;

`\begin{gathered} y=mx+b \\ 5=4(-1)+b \\ 5=-4+b \\ \text{Add 4 to both sides} \\ 5+4=-4+4+b \\ 9=b \end{gathered}`

Now we know the value of b and m, we can substitute them as follows;

`\begin{gathered} y=mx+b \\ m=4,b=9 \\ y=4x+9 \end{gathered}`