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What is the equation, in slope-intercept form, of line B?

Line A passes through point (−2, −1) and is perpendicular to the graph of y = −1/2x + 6.
Line B is parallel to line A and passes through the point (2, 1).

User Fofole
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1 Answer

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Answer:

Line A Equation

y = -(1)/(2)x -2

Line B Equation:

y = 2x - 3

Explanation:

We are given a line whose equation is:

y = -(1)/(2)x + 6 \cdots [1]

The general slope-intercept form of a line equation is:

y = mx + b

where
m is the slope and
b is the y-intercept

The line defined by equation [1] has a slope of
-(1)/(2) and a y-intercept of 6.

Lines which are parallel to each other will have the same slope,
m, but different y-intercepts,
b

Line A Equation

  • We are given that line A is parallel to the given line. This means that line A has the same slope of
    -(1)/(2)
  • We can therefore write down the equation of line A as:

    y = -(1)/(2)x + b \cdots[A]
  • To compute
    b, we note that the line A passes through (-2, -1). These are values of x and y which satisfy equation [A}
  • Plug in these values for
    x and
    y and solve for
    b to get the complete :
    -1 = -(1)/(2)\cdot(-2) + b\\\\-1 = 1 + b\\\\b = -2\\\\

  • So the equation for line A is

    y = -(1)/(2)x -2
  • One way to verify this is by actually graphing this equation using a graphing calculator and verifying it is indeed parallel to the given line and does pass through (-2, -1)
  • The first image provides this visual proof

Line B Equation

  • A line which is perpendicular to another line will have a slope equal to the negative of the reciprocal of the other line. Thus if one line has slope
    m, a perpendicular line will have slope
    -(1)/(m)
  • Since the given line has a slope of
    -(1)/(2) , line B should have a slope whish is the negative of the reciprocal of this number.

    \textrm{Reciprocal of } -(1)/(2) = -2}\\\\\textrm{Negative of -2 is 2}
  • So slope of line B is
    2 and we can write the equation of line B as:
    y = 2x + b \cdots[B]\\\\
  • We proceed to find
    b using the same technique as we did for line A:
    Line B passes through (2, 1)
  • Plug these values into equation [B}:

    1 = 2(2) + b\\\\1 = 4 + b\\\\b = -3
  • So equation of line B is

    y = 2x - 3
  • Graph for line B is attached as a second image

Hope that helps

What is the equation, in slope-intercept form, of line B? Line A passes through point-example-1
What is the equation, in slope-intercept form, of line B? Line A passes through point-example-2
User FreeZey
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