Solution assignment 10 Tangent line to graph

Give the equation of the line through the points:

$(1,2)$ and $(3,4)$

The slope of the line through the points:

$(x_1,y_1)$ and $(x_2,y_2)$

can be calculated as follows:

$m=\displaystyle\frac{y_2-y_1}{x_2-x_1}$

For the given points this yields:

$m=\displaystyle\frac{4-2}{3-1}=1$

Now we also know the slope of the line and thus we can use the following formula for the line:

$y-2=1(x-1)$

or:

$y=x+1$