Question

Complete the point-slope equation of the line through (2,3) and (7,4)

y-4=

Answer 1

Equation of line when it passes through points (x1,y1) and (x2,y2).

$\sf \large y - y_1= (x - x_1) \bigg( \dfrac{y_2 - y_1}{x_2 - x_1} \bigg)$

Here ,

$\sf \large \bigg( \dfrac{y_2 - y_1}{x_2 - x_1} \bigg) = m(slope \: of \: line)$

Now we have to find out the point-slope equation of the line through (2,3) and (7,4).

Let -

• x1 = 2
• x2 = 7
• y1= 3
• y2= 4

$\sf \implies y - 3= (x - 2) \bigg( \dfrac{4 - 3}{7-2} \bigg)$

$\sf \implies y - 3= (x - 2) \bigg( \dfrac{1}{5} \bigg)$

$\sf \implies 5(y - 3)= (x - 2)$

$\sf \implies 5y - 15= x - 2$

$\sf \implies 5y - x - 15 + 2= 0$

$\sf \implies 5y - x - 13= 0$

Answer :

the point-slope equation of the line through (2,3) and (7,4) => 5y-x-13=0

Answer 2

Answer:

Hello mate, answer is in photo!!