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Question #3) Standard: G.GPE.B.5 * 2 points ; Which equation represents a line parallel to the line whose equation is – 2x + 3y = -4 and passes through the point (1,3)? (1) y - 3 = -(x - 1) (3) y + 3 = - 3 (x + 1) (2) y – 3 = (x - 1) (4) y + 3 = ? (x + 1) O Option 1 O Option 2 Option 3 O Option 4

Respuesta :

The line:

[tex]-2x+3y=-4[/tex]

can be written as:

[tex]\begin{gathered} -2x+3y=-4 \\ 3y=2x-4 \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]

from this form we notice that its slope is 2/3.

We know that two lines are parallel if and only if their slopes are equal, this measn the lie we are looking for has slope 2/3 also.

Once we know the slope of the second line and since we know a point of it we can use the equation of a line:

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

Plugging the values we have that the equation we are looking for is:

[tex]y-3=\frac{2}{3}(x-1)[/tex]

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