Answer :

Answer:

The value of y is 4

The equation of line is y = x + 7   .

Step-by-step explanation:

Given as :

The points are

([tex]x_1[/tex], [tex]y_1[/tex]) = (- 3, y)

([tex]x_2[/tex], [tex]y_2[/tex]) = (- 9, -2)

The slope = m = 1

Now, The slope is calculated in points form

So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

I.e m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

or, 1 = [tex]\dfrac{- 2 - y}{- 9- (-3)}[/tex]

or, 1 = [tex]\dfrac{- 2 - y}{- 6}[/tex]

or, 1 × (-6) = - 2 - y

or, - 6 = - 2- y

or, y = - 2 + 6

∴ y = 4

So, The new points as

([tex]x_1[/tex], [tex]y_1[/tex]) = (- 3, 4 )

([tex]x_2[/tex], [tex]y_2[/tex]) = (- 9, -2)

So, the equation of line in slope - point form can be written as

y - [tex]y_1[/tex] = m ( x - [tex]x_1[/tex] )

i.e y - 4 = ( 1 ) × ( x - (-3) )

or, y - 4 = x + 3

∴ y = x + 3 + 4

Or, y = x + 7

So, The equation of line is y = x + 7

Hence The value of y is 4

And The equation of line is y = x + 7   . Answer

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