Question

How do I make an equation out of this line graph ?

Answer 1

The equation of a line in point-slope form is:

$y=mx+b$

Any point that belongs to this line is a solution to this equation. Looking at the graph we can see two points that belong to the line:

$(0,1)\text{ and }(5,3)$

By replacing x and y in the equation of the line with the values given by the points we can build two equations:

$\begin{gathered} y=mx+b \\ \text{From point (x,y)=(0,1) we get:} \\ 1=m\cdot0+b \\ 1=b \\ \text{From point (x,y)=(5,3) we get:} \\ 3=m\cdot5+b \end{gathered}$

So we have these two equations:

$\begin{gathered} 1=b \\ 3=5m+b \end{gathered}$

So according to the first equation b=1. If we replace this value in the second equation we can also find m:

$\begin{gathered} 3=5m+b \\ 3=5m+1 \\ 3-1=5m \\ 2=5m \\ m=\frac{2}{5} \end{gathered}$

Then the equation of the line that we are looking for and the answer to this question is:

$y=\frac{2}{5}x+1$