Question

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Answer 1

3x - 2y = 2

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, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m =
`(5-2)/(4-2)` =
`(3)/(2)` , then

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

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

using (2, 2 )

2 =
`(3)/(2)` (2) + c = 3 + c ( subtract 3 from both sides )

- 1 = c

y =
`(3)/(2)` x - 1 ← equation in slope- intercept form

multiply through by 2 to clear the fraction

2y = 3x - 2 ( subtract 3x from both sides )

- 3x + 2y = - 2 ( multiply through by - 1 )

3x - 2y = 2 ← in standard form