Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

equation of line with slope........?

Find an equation of the line with slope -2/3 that passes through (-1,2).

a. 2x + y - 1 = 0

b. x + 2y - 3 = 0

c. 2x + 3y - 4 = 0

d. x + 3y - 2 = 0

e. 4x + 2y + 4 = 0

d?

10 Answers

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  • 1 decade ago
    Favorite Answer

    Hi,

    First consider the equation of a straight line in point-slope form:

    y = m·x + b,

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

    So, let us plug in the value of the slope to get

    y = (-2/3)·x + b.

    Now, it is easy to solve for b just by plugging in the coordinates of the given point:

    2 = (-2/3)·(-1) + b

    2 = 2/3 + b

    or b = 4/3

    So our line is y = (-2/3)·x + 4/3

    Multiplying by 3 gives

    3y = -2·x + 4

    or 3·y + 2·x - 4 = 0,

    which is answer c.

    If someone was in a hurry and didn't want to go through all of that, they could have just plugged in x = -1 and y = 2 into each equation until they got to Answer C.

    James :-)

  • Raichu
    Lv 6
    1 decade ago

    To find the slope of the line, make y the subject of the equation. The coefficient of x is then the slope. E.g., for c, you can rewrite it as:

    y = -(2/3)x + 4.

    That means the slope is -2/3.

    To check whether a line goes through a particular point, you have to understand what a line equation means.

    A line is a set of points. The equation of the line is a formula that tells you which points. An equation is a sentence. The sentence y = 2x means "the value of y is two times the value of x". That means the line y=2x contains just those points whose y value is two times their x value. If a point, like (100.200), satisfies that condition, then it's on the line. If it doesn't, like (100,199), then it's not on the line.

    Back to your question, the way you tell if a line passes through a particular point is to see whether those values of x and y make the sentence true. So for a, you have

    -2 + 2 -1 = 0.

    Is that a true statement or a false one? The left side evaluates to -1, and -1 is not 0, so it's false. Therefore the point (-1,2) is not on that line.

  • Anonymous
    1 decade ago

    y = mx + b where m is the slope and b is the y-intercept

    You have to solve for y, and since the answer c was already given, we'll do that one:

    2x + 3y - 4 = 0

    3y = -2x + 4

    y = -2x/3 + 4/3

    so the slope is correct. Let's try the x and y values for the given point:

    2 = -2(-1)/3 + 4/3= 2/3 + 4/3 = 6/3 = 2

    s'aright!

  • 1 decade ago

    The equation of any line passing through a point (x',y') and having slope m is given by:-

    y-y' = m (x-x')

    Now slope is -2/3 and the point is (-1,2):: substitute these values in the above equation.

    Y-2 = -2/3[x-(-1)]

    or y-2 = -2/3(x+1)

    or 3y-6 = -2x-2

    or 2x+3y-4=0

    Therefore c. is the correct answer.

    Source(s): primrosh
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  • 1 decade ago

    no the answer is c

    becos if u re-arrange the eqution from 2x + 3y - 4 =0

    then u make y the subject of the formula: y= -2/3x + 4

    the slope or gradient is -2/3 and the y-intercept is 4

  • Anonymous
    1 decade ago

    slope-intercept form is y=mx + b

    the given is m/slope=-2/3 and points(-1,2)

    so,

    y=mx+b

    y=-2/3x+b

    using the points (-1,2) which is(x,y),

    2=-2/3(-1)+b

    2=2/3+b

    2-2/3=b

    4/3=b

    then,

    answer would be y=-2/3x+4/3

    changing to standard form which is Ax+By+C=0,

    2/3x+y-4/3=0

    standard form has no fractions so we need to cancel out the denominators by,

    3(2/3x+y-4/3)=0

    the equation would become...

    2x+3y-4=0

    So finally, the answer is letter C!

    Good luck!

  • Anonymous
    1 decade ago

    equation: y=mx+c

    given slope, m= -2/3

    x= -1

    y= 2

    2=(-2/3)(-1) + c

    c= 2-2/3

    c= 4/3

    the equation is : y= -2/3 x + 4/3

    3y= -2x + 4

    3y+2x-4=0

    the answer is C.

  • 1 decade ago

    y-y1=m(x-x1)

    y-2=(-2/3)(x+1)

    y = -2x/3 + 4/3

    3y = -2x + 4

    3y + 2x = 4

    2x + 3y - 4 = 0

    c

  • Anonymous
    1 decade ago

    c

    only slope of c is -2/3

    and -2+6-4=0

  • 1 decade ago

    its not d.its C!

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