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:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]We are given the points (-1,1) and (2,3). Calculating the slope:
[tex]\displaystyle m=\frac{3-1}{2+1}=\frac{2}{3}[/tex]Once we know the value of the slope, the equation of the line is:
[tex]y=\frac{2}{3}x+b[/tex]The value of b can be determined by substituting (x,y) for one of the given points, for example (2,3):
[tex]\begin{gathered} 3=\frac{2}{3}\cdot2+b \\ \text{Operating:} \\ 3=\frac{4}{3}+b \end{gathered}[/tex]Solving for b:
[tex]b=3-\frac{4}{3}=\frac{9-4}{3}=\frac{5}{3}[/tex]The equation of the line is, finally:
[tex]y=\frac{2}{3}x+\frac{5}{3}[/tex]There are other forms to write the equation of a line, we used the slope-intercept form
