Question

This is lines, functions and systems. Graph the line with slope 1 passing through the point (4, 2).

Answer 1

To graph the line we need two points; we already have one the point (4,2) now we need to find another one; to do this we get the equation of the line given by:

$y-y_1=m(x-x_1)$

where m is the slope and (x1,y1) are a point throught the line. Plugging the values given we have:

$\begin{gathered} y-2=1(x-4) \\ y-2=x-4 \\ y=x-4+2 \\ y=x-2 \end{gathered}$

Now we give a value to x and find the corresponding y. If x=0, then:

$y=-2$

hence we have the point (0,-2).

Now that we have two points (0,-2) and (4,2) we graph them on the plane and join them with a straight line, hence the graph is: