What is the equation of the line passing through (-3,-2 ) and (1, -5)?

sooxicyiy

sooxicyiy

Answered question

2022-09-05

What is the equation of the line passing through (-3,-2 ) and (1, -5)?

Answer & Explanation

Mekhi Parker

Mekhi Parker

Beginner2022-09-06Added 18 answers

y = - 3 4 x - 17 4
Explanation:
The equation of a line in point-slope form is.
| 2 2 y - y 1 = m ( x - x 1 ) 2 2 | ̲ ¯
where m represents the slope and ( x 1 , y 1 ) a point on the line a point on the line
To calculate m, use the gradient formula
| 2 2 m = y 2 - y 1 x 2 - x 1 2 2 | ̲ ¯
where ( x 1 , y 1 ) , ( x 2 , y 2 ) are 2 coordinate points are 2 coordinate points
The 2 points here are (-3 ,-2) and (1 ,-5)
let ( x 1 , y 1 ) = ( - 3 , - 2 ) and ( x 2 , y 2 ) = ( 1 , - 5 )
m = - 5 - ( - 2 ) 1 - ( - 3 ) = - 3 4 = - 3 4
We can use either of the points (-3 ,-2), (1 ,-5) as the point on the line since the line passes through both of them.
Using ( x 1 , y 1 ) = ( 1 , - 5 ) and m = - 3 4 and Using ( x 1 , y 1 ) = ( 1 , - 5 ) and m = - 3 4
Substitute these values into the equation.
y - ( - 5 ) = - 3 4 ( x - 1 )
y + 5 = - 3 4 ( x - 1 ) in point-slope form
Distributing and simplifying gives an alternative version of the equation.
y + 5 = - 3 4 x + 3 4
y = - 3 4 x + 3 4 - 5
y = - 3 4 x - 17 4 in slope-intercept form

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