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)=(d-b)/(c-a)(x-a)`

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

`(y-(-1))=(5-(-1))/(6-2)(x-2)\\\\\Rightarrow\ (y+1)=(6)/(4)(x-2)`

`\\\\\Rightarrow\ (y+1)=(3)/(2)(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=(3)/(2)x-3\\\\\Rightarrow\ y=\frac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2*4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}]`