Question

Find the equation in standard form of the line passing through the points (3,-4) and (5,1)

Answer 1

Answer: $5x-2y=23$

Step-by-step explanation:

The equation of a line passing through (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Also , the equation of a line in standard form is given by :-

$Ax+By=C$

Then , the equation of a line passing through points (3,-4) and (5,1) will be :-

$(y-1)=\dfrac{-4-1}{3-5}(x-5)$

$\Rightarrow\ (y-1)=\dfrac{-5}{-2}(x-5)$

$\Rightarrow\ (y-1)=\dfrac{5}{2}(x-5)$

Convert into standard form.

$\Rightarrow\ 2(y-1)=5(x-5)$

$\Rightarrow\ 2y-2=5x-25$

$\Rightarrow\ 25-2=5x-2y$

$\Rightarrow\ 5x-2y=23$

Hence, the standard form of the line passing through the points (3,-4) and (5,1) : $5x-2y=23$

Answer 2

Answer:

5x-2y=23

Step-by-step explanation:

The line is passing through the points (3,-4) and (5,1).

Thus, we have

$x_1=3,y_1=-4,x_2=5,y_2=1$

The slope of the line is given by

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1+4}{5-3}\\\\m=\frac{5}{2}$

The point slope form of a line is given by

$y-y_1=m(x-x_1)\\\\y+4=\frac{5}{2}(x-3)\\\\y+4=\frac{5}{2}x-\frac{15}{2}\\\\2y+8=5x-15\\\\5x-2y=23$

Thus, the standard form of the line is given by 5x-2y=23