Respuesta :

penfila11Pen
Hey there :)

y = [tex] \frac{2}{3}x + 4 [/tex]

Since this line is parallel to the line to be found, both have the same slope: [tex] \frac{2}{3} [/tex]

Coordinates: ( - 9 , - 2 )

y - ( -2 ) = [tex] \frac{2}{3} [/tex] ( x - ( -9 ) )
[tex] y + 2 = \frac{2}{3} x + 6 [/tex]
[tex] y = \frac{2}{3} x + 6 - 2[/tex]

[tex] y = \frac{2}{3}x + 4 [/tex]


MarkV
Hi there! The answer is y = 2/3x + 4

When the line we are looking for is parallel to y = 2/3x + 4, the slope is the same as in the line mentioned before. Hence, we get the following formula:
[tex]y = \frac{2}{3}x + b [/tex]

In this equation, b represents a number. Since the line passes through the point (-9, -2) we can plug in the coordinates into the formula. Then we get the following:
[tex]\frac{2}{3} * -9 + b = -2 [/tex]
[tex]-6 + b = -2[/tex]

Now we add 6 to both sides of the equation
[tex]b = 4[/tex]

We've now found our answer, the formula of the line, which is:
y = 2/3x + 4

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