Anonymous

# 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?

Relevance

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,

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 :-)

• 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

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!

• 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
• 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

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,

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

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

• 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