Question

Enter the equation of the line in the form y = mx + b where m is the slope and b is the y-intercept.

Answer 1

We are asked to determine the equation of the given line. To do that we need to remember that the equation of the line is given by:

`y=mx+b`

Where "m" is the slope and "b" the y-intercept. The y-intercept is the point where the line touches the y-axis. From the graph, we can notice that the y-intercept is -2, therefore, b = -2. Replacing in the line equation:

`y=mx-2`

To determine the value of the slope, we can replace any point through which the line passes. Taking the point (x,y) = (1,1). Replacing in the line equation:

`1=m(1)-2`

Solving the operations:

`1=m-2`

Adding 2 to both sides:

`\begin{gathered} 1+2=m-2+2 \\ 3=m \end{gathered}`

Replacing in the equation:

`y=3x-2`

And thus we get the equation of the line.