What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)? 3x − 4y = −17

Question

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)

in progress 0
Alice 5 days 2021-09-13T14:07:38+00:00 2 Answers 0

Answers ( )

    0
    2021-09-13T14:08:43+00:00

    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:

    m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}

    Then, the requested line will be of the form:

    y = - \frac {4} {3} x + b

    To find “b” we substitute the given point:

    2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2

    Finally, the line is:

    y = - \frac {4} {3} x-2

    By manipulating algebraically we have:

    y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6

    Answer:

    Option D

    0
    2021-09-13T14:08:52+00:00

    Answer: last option.

    Step-by-step explanation:

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

    y=mx+b

    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:

    m=\frac{-1-3}{3-0}=-\frac{4}{3}

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

     m=-\frac{4}{3}

    Substitute the slope and the point (-3, 2) into y=mx+b and solve for “b”:

     2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2

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

    y=-\frac{4}{3}x-2

    Rewriting it in Standard form, you get:

    y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )