Question

How does this work? I’ve been trying to figure it out but have not been able to.

Answer 1

We have to graph a linen with slope 2 and that contains the point (-3,-1).

We can use this information to write the equation of the line in slope-point form:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-(-1)=2(x-(-3)) \\ y+1=2(x+3) \\ y=2x+2\cdot3-1 \\ y=2x+6-1 \\ y=2x+5 \end{gathered}`

We can graph the line without knowing the equation, only knowing a single point of the line and the slope:

- We plot the point (x0,y0).

- We calculate a second point where we add one unit to x-coordinate from x0 and m units to the y-coordinate: (x0+1, y0+m).

NOTE: This is because, if we have an slope m, this means that y increases m units for each unit increase in x. We can write it for any point generally as (x0+k, y0+k*m).

Then, we plot the point (-3,-1).

The second point of thte line to plot it will be:

`(x_0+1,y_0+m)=(-3+1,-1+2)=(-2,1)`

Then, with two points of the line we draw the line that pass through those points (-3,-1) and (-2,1):