Question

Determine the equation for the line that passes through (2,-1) and (6,5)
Write in point slope form
Write in slope intercept form
Write in standard form

Answer 1

Answer with explanation:

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

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

Equation of line passing through (2,-1) and (6,5) is given by :-

$(y-(-1))=\dfrac{5-(-1)}{6-2}(x-2)\\\\\Rightarrow\ (y+1)=\dfrac{6}{4}(x-2)$

$\\\\\Rightarrow\ (y+1)=\dfrac{3}{2}(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=\dfrac{3}{2}x-3\\\\\Rightarrow\ y=\dfrac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2\times4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}]$