Question

What is the equation of the line, in standard form, connecting points (2, -3) and (4, 4)?

Responses

7x−2y−26=07 x minus 2 y minus 26 is equal to 0

7x+y−13=07 x plus y minus 13 is equal to 0

7x−2y−20=07 x minus 2 y minus 20 is equal to 0

2x−2y−7=02 x minus 2 y minus 7 is equal to 0

3x−y+10=0

Answer 1

7x - 2y - 20 = 0

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, 4 )

m =
`(4-(-3))/(4-2)` =
`(4+3)/(2)` =
`(7)/(2)` , then

y =
`(7)/(2)` x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 4 )

4 =
`(7)/(2)` (4) + c = 14 + c ( subtract 14 from both sides )

- 10 = c

y =
`(7)/(2)` x - 10 ← in slope- intercept form

multiply through by 2

2y = 7x - 20 ( subtract 2y from both sides )

0 = 7x - 2y - 20 , that is

7x - 2y - 20 = 0 ← required equation