If you have a graph with a line and you want the equation which represents this line.
You can choose 2 points along the line.
For instance.
These points have coordinates (x1,y1) and (x2,y2).
By means of their values we can compute the slope m of the line.
Remember that, the general straight line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For instance, lets suppose that
[tex]\begin{gathered} (x_1,y_1)=(1,3) \\ (x_2,y_2)=(4,7) \end{gathered}[/tex]hence, the slope is
[tex]\begin{gathered} m=\frac{7-3}{4-1} \\ m=\frac{4}{3} \end{gathered}[/tex]and the equation for this particular case is
[tex]y=\frac{4}{3}x+b[/tex]the only thing to find is the y-intercept b. This b can be computed by using one of the 2 points.
For instance, if we take point (1,3) in our example, and subtitute the coordinates into the above formula, we have
[tex]3=\frac{4}{3}(1)+b[/tex]and by means of this, we can find b:
[tex]\begin{gathered} 3=\frac{4}{3}+b \\ b=3-\frac{4}{3} \\ b=\frac{9}{3}-\frac{4}{3} \\ b=\frac{5}{3} \end{gathered}[/tex]and finally, the line equation wiil be
[tex]y=\frac{4}{3}x+\frac{5}{3}[/tex]
