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Triangle QRS is similar to triangle TUV. Write the equation, in slope-intercept form, of the side of triangle QRS that is parallel to UV. You must show all work to receive credit. (10 points)

Triangle QRS is similar to triangle TUV Write the equation in slopeintercept form of the side of triangle QRS that is parallel to UV You must show all work to r class=

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Answer:

Side of ΔQRS parallel to UV is RS

Equation of line RS:
[tex]\boxed{y = x + 9}[/tex]

Step-by-step explanation:

  • The slope-intercept form of a line is given by
    [tex]y = mx + c[/tex] [tex]\text{where m is the slope and c is the y-intercept}[/tex]
  • The slope is calculated using the following formula
    [tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]
    [tex]\text{where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the straight line}[/tex]
  • The side in ΔQRS that is parallel to UV is side RS
  • Therefore we have to find the slope-intercept form of line RS
  • Take two points on RS, say S( -8, 1) and R(- 2, 7)
    [tex]\text{Slope m = $\dfrac{7 - 1}{-2 - (-8)}$ }\\\\= $\dfrac{6}{-2 + 8}$\\\\= \dfrac{6}{6}\\\\m = 1[/tex]

  • So the equation of the line RS is
    y = 1x + c
  • To find the y-intercept c, take any point on the line (x, y) and substitute  these values into the slope equation
  • Take Point R(-2, 7)
  • Substituting y = 7, x = -1 gives
    7 = 1 (-2) + c
    7 = -2 + c
    7 + 2 = 2 + 2 + c   (add 2 both sides)
    9 = 0 + c
    9 = c
     or
    c = 9
  • Therefore the equation of RS is
    y = 1x + 9

    which can be written as
    [tex]\boxed{y = x + 9}[/tex]

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