This Post Has 6 Comments

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

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2. 6x-y=19

   Step-by-step explanation:

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3. 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

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4. 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)

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5. 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

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6. [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]

   Reply