Which equation represents the line that passes through the points (6,-3) and (-4,-9)?

d1di9u01

d1di9u01

Answered question

2023-02-16

Which equation represents the line that passes through the points (6,-3) and (-4,-9)?

Answer & Explanation

Darien Jennings

Darien Jennings

Beginner2023-02-17Added 9 answers

We can determine the slope because we have two points to work with, and we can then use the slope, either point, and the point-slope formula to determine the equation for the line.
The slope can be found by using the formula: m = y 2 - y 1 x 2 - x 1
Where #m# is the slope and ( x 1 , y 1 ) and ( x 2 , y 2 ) are the two points on the line.
Substituting the two points from the problem gives:
m = - 9 - - 3 - 4 - 6
m = - 9 + 3 - 4 - 6
m = - 6 - 10
m = 6 10 = 3 5
Now we have the slope and can use either point and the point-slope formula to find the equation for the line:
The point-slope formula states: ( y - y 1 ) = m ( x - x 1 )
Where m is the slope and ( x 1 y 1 ) is a point the line passes through.
One of the points and the slope we calculated are substituted to produce
( y - - 9 ) = 3 5 ( x - - 4 )
( y + 9 ) = 3 5 ( x + 4 )
By figuring out y , we may transform to the more well-known slope-intercept form:
y + 9 = 3 5 x + ( 3 5 × 4 )
y + 9 = 3 5 x + 12 5
y + 9 - 9 = 3 5 x + 12 5 - 9
y + 0 = 3 5 x + 12 5 - ( 9 × 5 5 )
y = 3 5 x + 12 5 - 45 5
y = 3 5 x - 33 5

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