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Find the equation of a line that joins the midpoint of (7, 3) and (9, -7) and the y-intercept of
5x – 6 = 2y.

y = x - 3

Step-by-step explanation:

Use the midpoint formula

Given (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ (x₁ + x₂ ), (y₁ + y₂ ) ]

Here (x₁, y₁ ) = (7, 3) and (x₂, y₂ ) = (9, - 7), thus

midpoint = [ (7 + 9), (3 - 7 ) ] = (8, - 2)

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The equation of a line in slope- intercept form is

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

Rearrange 5x - 6 = 2y into this form by dividing all terms by 2

y = x - 3 ← in slope- intercept form

with y- intercept c = - 3 ⇒ (0, - 3 )

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Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂, x₁ )

with (x₁, y₁ ) = (8, - 2) and (x₂, y₂ ) = (0, - 3)

m = = =

y = x - 3 ← equation of line

step-by-step explanation:

; fx

the translated point is (5,2)