Mathematics

Question

Consider the graph of the line y = .5x- 4 and the point
(-4,2).
The slope of a line parallel to the given line is
(1/
24
A point on the line parallel to the given line, passing
through (-4, 2), is (0,4) 4.
The slope of a line perpendicular to the given line is
-2
A point on the line perpendicular to the given line,
passing through (-4,2), is

2 Answer

  • Answer:

    slope of parallel line and perpendicular line are 5 and -1/5 espectively

    equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively

    Step-by-step explanation:

    y = 5x - 4 is in the form

    y = mx + c

    where m is the slope of the line and c is the y intercept of thr line

    therefore slope of the line = 5 and y intercept = -4

    when an another line is parallel to the given line then the slope of both the lines are equal

    therefore the slope the parallel line = 5

    equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]

    given [tex](x_{1} ,y_{1})[/tex]= (-4,2)

    therefore equation of line y-2 = 5(x+4)

    therefore y = 2+ 5x+20

    y = 5x + 22is the eqaution of required line.

    when two lines are perpendiculer then

    [tex]m_{1} m_{2}=-1[/tex]

    where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore

    m×5=-1

    therefore m= [tex]\frac{-1}{5}[/tex]

    therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]

    [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]

  • Answer:

    1/2

    (0,4)

    -2

    (-2,-2)

    Step-by-step explanation:

    edge

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