Question

Write an equation of the line that passes through (-1,1) and (2,3)

Answer 1

Equation of a Line

The equation of the line in slope-intercept form is:

y=mx+b

Where:

m = slope

b = y-intercept.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

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

We are given the points (-1,1) and (2,3). Calculating the slope:

`\displaystyle m=(3-1)/(2+1)=(2)/(3)`

Once we know the value of the slope, the equation of the line is:

`y=(2)/(3)x+b`

The value of b can be determined by substituting (x,y) for one of the given points, for example (2,3):

`\begin{gathered} 3=(2)/(3)\cdot2+b \\ \text{Operating:} \\ 3=(4)/(3)+b \end{gathered}`

Solving for b:

`b=3-(4)/(3)=(9-4)/(3)=(5)/(3)`

The equation of the line is, finally:

`y=(2)/(3)x+(5)/(3)`

There are other forms to write the equation of a line, we used the slope-intercept form