Complete the point-slope equation of the line through (1,0) (6,−3)

Question

asked Sep 8, 2024 165k views

2 Answers

Ghasem Sadeghi · Answer 1 · 2024-09-10T21:23:30+0000

Required answer: y + 3 = -3/5(x - 6)

Detailed explanation:

First, I'll find the slope of the line through the two points:

$\bf{m=(y_2-y_1)/(x_2-x_1)}$

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$\bf{m=(-3-0)/(6-1)}$

$\bf{m=-(-3)/(5)}$

$\bf{m=-(3)/(5)}$

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Now, we write our point-slope equation:

$\bf{y-y_1=m(x-x_1)}$

Plug in the data:

$\bf{y-(-3)=-(3)/(5)(x-6)}$

$\boxed{\bf{y+3=-(3)/(5)x(-6)}}$

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Luishg · Answer 2 · 2024-09-12T03:10:54+0000

Answer:

y + 3 = -
(3)/(5) (x - 6 )

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m =
(y_(2)-y_(1) )/(x_(2)-x_(1) )

with (x₁, y₁ ) = (1, 0 ) and (x₂, y₂ ) = (6, - 3 )

m =
(-3-0)/(6-1) =
(-3)/(5) = -
(3)/(5)

we now require a point on the line

given 2 points we can use either as the point (a, b )

using (a, b ) = (6, - 3 ) , then

y - (- 3) = -
(3)/(5) (x - 6) , that is

y + 3 = -
(3)/(5) (x - 6) ← in point- slope form