Question

How do you solve graphs which represent a line and make an equation from a line on a graph?

Answer 1

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

`y=mx+b`

where m is the slope and b the y-intercept. The slope formula is

`m=(y_2-y_1)/(x_2-x_1)`

For instance, lets suppose that

`\begin{gathered} (x_1,y_1)=(1,3) \\ (x_2,y_2)=(4,7) \end{gathered}`

hence, the slope is

`\begin{gathered} m=(7-3)/(4-1) \\ m=(4)/(3) \end{gathered}`

and the equation for this particular case is

`y=(4)/(3)x+b`

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

`3=(4)/(3)(1)+b`

and by means of this, we can find b:

`\begin{gathered} 3=(4)/(3)+b \\ b=3-(4)/(3) \\ b=(9)/(3)-(4)/(3) \\ b=(5)/(3) \end{gathered}`

and finally, the line equation wiil be

`y=(4)/(3)x+(5)/(3)`