Question

Point A is (2,-1) and point B is (4,5). What is the equation of the line passing through these two points?

• A. $y=3x+7$
• B. $y=3x-7$
• C. $y=3x-3$

Answer 1

The correct option is B $y=3x-7$

$\underset{–}{ConceptInvolved:}$

If a line passes through a point (a,b) and has slope 'm', then the equation of the line would be given by Point slope form as:
$(y-b)=m(x-a)$

If we are given two points $(x_1,y_1)$ and $(x_2,y_2)$, then
'm' can be written as:
$m=\frac{y_2-y_1}{x_2-x_1}$

Equation of the line can be written as when two points are given:
$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\underset{–}{Method:}$

First we need to find the slope of the line that passes through the points A(2,-1) and B(4,5).
Slope $=m=\frac{5-(-1)}{4-2}=\frac{6}{2}=3$

Putting these values in Point slope form of the line taking point as A(2,-1).
$y-(-1)=3\times (x-2)$
$y+1=3x-6$
$y=3x-7$

Putting the values in Point slope form of the line taking point as B(4,5).
$y-5=3\times (x-4)$
$y-5=3x-12$
$y=3x-7$