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What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?

3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6

Visible line: (0,3)(3,-1)

Respuesta :

carlosego

For this case we have that by definition, if two lines are parallel their slopes are equal.

The line given for the following points:

(0,3) and (3, -1). Then the slope is:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}[/tex]

Then, the requested line will be of the form:

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

To find "b" we substitute the given point:

[tex]2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2[/tex]

Finally, the line is:

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

By manipulating algebraically we have:

[tex]y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6[/tex]

Answer:

Option D

luisejr77

Answer: last option.

Step-by-step explanation:

 The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:

[tex]m=\frac{-1-3}{3-0}=-\frac{4}{3}[/tex]

Since the other line is parallel to this line, its slope must  be equal:

 [tex]m=-\frac{4}{3}[/tex]

Substitute the slope and the point (-3, 2) into [tex]y=mx+b[/tex] and solve for "b":

 [tex]2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2[/tex]

Then, the equation of the other line in Slope-Intercept form is:

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

Rewriting it in Standard form, you get:

[tex]y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6[/tex]

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