Answer: Equation of line in point slope form,
[tex]y + 1 = 5 ( x - 2 )[/tex]
And, Equation of line in standard form,
[tex]5 x - 6 y = 16[/tex]
Step-by-step explanation:
Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,
Then the equation of line,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]
Thus, the equation of the given line,
[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)
⇒ [tex]6(y+1)= 5(x-2)[/tex]
⇒ 6 y + 6 = 5 x - 10
⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )
⇒ 6 + 10 = 5x - 6y ( By adding 10 on both sides )
⇒ 16 = 5x - 6y
⇒ 5 x - 6 y = 16 ------(2)
Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]
Thus, equation (1) shows the in slope form of the line.
And, standard form of the line is ax + by = c where a, b and c are the integers.
Thus, equation (2) shows the standard form of the given line.
