What is an equation in point-slope form of the line that passes through (-7, 1) and (-3, 9)

Question

asked Jun 3, 2024 126k views

2 Answers

Ganesh Kudva · Answer 1 · 2024-06-07T23:47:51+0000

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Here we go ~

First, calculate the slope of line joining points (-7 , 1) and (-3 , 9) :

$\qquad \sf  \dashrightarrow \: m = (y2 -y1 )/(x2 - x1)$

$\qquad \sf  \dashrightarrow \: m = (9 - 1)/( - 3 - ( - 7))$

$\qquad \sf  \dashrightarrow \: m = (8)/( - 3 + 7)$

$\qquad \sf  \dashrightarrow \: m = (8)/( 4)$

$\qquad \sf  \dashrightarrow \: m = 2$

Slope of the line (m) = 2

Equation of line in point slope form :

$\qquad \sf  \dashrightarrow \: y - y1 = m(x - x1)$

[ Put in the values ~ ]

$\qquad \sf  \dashrightarrow \: y - 9 = 2(x - ( - 3))$

$\qquad \sf  \dashrightarrow \: y - 9 = 2(x + 3)$

[ That's our required equation in point slope form ]

But it can be simplified further, it depends on it, if that's asked or not.

$\qquad \sf  \dashrightarrow \: y - 9 = 2x + 6$

$\qquad \sf  \dashrightarrow \: y = 2x + 6 + 9$

$\qquad \sf  \dashrightarrow \: y = 2x + 15$