Line t passes through (4,5) and is perpendicular to the line shown on the coordinate grid.

Line t passes through (4,5) and is perpendicular to the line shown on the coordinate grid.


[tex]Line t passes through (4,5) and is perpendicular to the line shown on the coordinate grid.[/tex]

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  1. option d. 6x − y = 19

    step-by-step explanation:

    step 1

    find the slope of the given line that passes through the points (0,3) and (6,2)

    m=(2-3)/(6-0)

    m=-1/6

    step 2

    find the slope of the line t

    we know that

    if two lines are perpendicular, then the product of their slopes is equal to -1

    m1*m2=-1

    we have

    m1=-1/6

    substitute

    (-1/6)*m2=-1

    m2=6

    step 3

    find the equation of the line t

    the equation of the line into point slope form is equal to

    y-y1=m(x-x1)

    we have

    m=6

    point (4,5)

    substitute

    y-5=6(x-4)

    y=6x-24+5

    y=6x-19

    6x-y=19

  2. 7x − y = 23

    Step-by-step explanation:

    The equation of line shown using the two points would be:

    We know perpendicular line's slope (the number before x) would be "negative reciprocal of this, hence the equation of the perpendicular line would take the form:

    Since it goes through (4,5), we can plug in 4 in x and 5 in y to figure out b:

    So the equaiton is  y = 7x - 23

    In standard form it is: 7x - y = 23

  3. 6x − y = 19

    Step-by-step explanation:

    x + 6y = 114

    4 + 6(5) = 114

    34 = 114 (false)

    −6x − y = 19

    -6(4) - 5 = 19

    -29 = 19 (false)

    x − 6y = −11

    4 - 6(5) = -11

    -26 = -11 (false)

    6x − y = 19

    6(4) - 5 = 19

    19 = 19 (true)

  4. For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

    Where:

    m: It is the slope of the line

    b: It is the cut-off point with the y axis

    To find the slope of the plotted line, we need two points, according to the image we have:

    The slope is:

    Therefore, the equation is of the form:

    We substitute one of the points and find "b":

    Finally, the equation of the graph is:

    By definition, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

    Thus, the equation of the line t is of the form:

    y = 5x + b

    We substitute the point and find "b":

    Finally, the equation is of the form:

    Option A

  5. [tex]5x-y=15[/tex]

    Step-by-step explanation:

    step 1

    Find the slope of the given line

    The formula to calculate the slope between two points is equal to

    [tex]m=\frac{y2-y1}{x2-x1}[/tex]

    we have

    (0,3) and (5,2)

    substitute

    [tex]m=\frac{2-3}{5-0}[/tex]

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

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

    step 2

    Find the slope of the line t

    we know that

    If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

    so

    [tex]m_1*m_2=-1[/tex]

    we have

    [tex]m_1=-\frac{1}{5}[/tex] ---> slope of the given line

    [tex]m_2=5[/tex] ----> slope of line t

    step 3

    Find the equation of the line t in point slope form

    [tex]y-y1=m(x-x1)[/tex]

    we have

    [tex]m=5[/tex]

    [tex]point\ (4,5)[/tex]

    substitute

    [tex]y-5=5(x-4)[/tex]

    step 4

    Convert to slope intercept form

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

    isolate the variable y

    [tex]y-5=5x-20[/tex]

    [tex]y=5x-20+5[/tex]

    [tex]y=5x-15[/tex]

    step 5

    Convert to standard form

    The equation in standard form is equal to

    [tex]Ax+By=C[/tex]

    where

    A is a positive integer

    B and C are integers

    so

    [tex]y=5x-15[/tex]

    subtract y both sides

    [tex]0=5x-15-y[/tex]

    Adds 15 both sides

    [tex]15=5x-y[/tex]

    Rewrite

    [tex]5x-y=15[/tex]

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