On solving the provided question the equation of line segment is [tex]3y = x+11 OR y = 1/3x + 11/3[/tex]
An equation in algebra is a condition on a variable. Only for a certain value of the variable does it satisfy. This indicates that the equation 2x - 5 = 13 can only be met when x = 9. Polynomial equations and linear equations are two significant kinds of equations that are taken into account in algebra. One-variable polynomial equations can be expressed as P(x) = 0, where P is a polynomial and ax + b = 0 is the standard form for linear equations. Here, the variables a and b are used.
Let y=m x + c be the slope intercept form of the equation.
Here, the slope m and the y-intercept c are unknown.
What is known is that this goes through (x 1, y 1) and (x 2, y 2), two coordinate pairs.
Consequently, we have three equations.
[tex]y=mx+c.........1\\ y1=mx1+c....2\\ y2=mx2+c ......3[/tex]
now let's delete m and c using these.
subtracting (2) from (1), we get [tex](y-y1)=m(x-x1) ......(4)[/tex]
and subtracting (2) from (3), we get[tex](y-2-y1)=m(x2-x1) ......(5)[/tex]
[tex]\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} \\\\\frac{y-3}{4-3} = \frac{x+2}{1+2} \\\\y-3 = \frac{x+2}{3}\\ 3y-9 = x+2\\3y = x+11\\OR\\y = 1/3x + 11/3[/tex]
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