What would be an equation for a line passing thru (1, -2) and (4, -6)?

Question

could be one of these following answers...

4x - 3y - 2 = 0

4x + 3y + 2 = 0

4x - 3y + 2 = 0

4x + 3y - 2 = 0

or is none of these

Answer 1

What you need to do to solve this is to plug the coordinates into the equation and see if they work. If there is a formula that both sets work for, then that is the correct answer.

Answer 2

There are several ways to do this, but I feel the best way is as follows.

The equation for a line is y = mx + b, where m is the slope and b is the y-intercept. So we need to "rearrange" the above four equations into that format for simplicity:

1. y = 4/3x - 2/3
2. y = -4/3x - 2/3
3. y = 4/3 x + 2/3
4. y = -4/3x + 2/3

You can see that all four equations are very similar, but the differences are huge (in terms of positive and negative values).

Now go back to the question, your x values are 1 and 4. Your y values are -2 and -6. A slope is the change in y values (delta y) over the change in x values (delta x) (or rise, the y-coordinates, over run, the x-coordinates). So doing the math, you can see that the change in y values is: -6 - (-2) = -4. The change in x values is: 4 - 1 = 3. That gives a slope of -4/3. If you look at my rearranged equations above, only equations 2 and 4 have a slope of -4/3, so we can immediately eliminate the first and third choice as possible answers.

To determine if the answer is equation 2 or 4, we have to calculate the y-intercept. The y-intercept is the value when x = 0. Calculating this is trickier. You could graph the above line and if you did, you'd see that the y-intercept is leaning towards the negative, or -2/3 value. But how good are your graphing skills? The best way is to plug in values into the rearranged equations above. For example, take the (1, -2) coordinate. Plug that into equation 4:

4. y = -4/3x + 2/3
If y = -2 and x = 1, then:
-2 = -4/3 + 2/3
-2 = -2/3
-6 = -2
Uh... no. -6 does not equal -2.

Let's look at equation 2 and do the same thing:

2. y = -4/3x - 2/3
If y = -2 and x = 1, then:
-2 = -4/3 -2/3
-2 = -6/3
-6 = -6
Yes! -6 does equal -6!

We can even plug in the other coordinate (4, -6):

2. y = -4/3x - 2/3
If y = -6 and x = 4, then:
-6 = -16/3 - 2/3
-6 = -18/3
-18 = -18
Yes! Works for this as well!

So based on the fact that said graphing shows a negative y-intercept, that equation 2 mathematically is valid for both coordinates, and that we mathematically determined the slope to match equation 2, equation 2 is the answer.

Hope this helps!

P.S. The person above my answer who said "none of the equations" and the person below me who said equation 4 both are on the right tracks, but both performed addition/subtraction errors. They have an error in converting the proper negative values. If they did the same work, but added/subtracted properly, they'd come up with equation 2. The beauty is that they are showing you other ways to answer this question, but you do have to watch your math and add/subtract correctly as even the slightest error will throw you off.

Answer 3

The slope m of the line:
m = Difference in Y-coordinates/ Difference of X-coordinates
=(-2+6)/(1-4) = - 4/3.
The equation of the line is y-b =m(x-a).
Here, y+2 = (- 4/3)(x-1) Or 3y +6 = - 4x +4.
which leads to : 4x+3y +2 =0. Answer.
Verify: OK

Answer 4

First, you need to find the gradient (or some call it slope) of the line because you will need a gradient to form an equation.

And, you need to know the formula to form an equation for a line:
y - y1 = m (x - x1)

::: m is the gradient and x1,y1 is the coordinate of a point on the line:::

So, to find gradient, use (y1-y2) / (x1-x2)
=[-6-(-2)] / [4-1]
= (-6+2) / 3
= - 4/3

To find the equation of the line,
y - (-2) = -4/3 (x - 1)
y + 2 = -4/3x + 4/3
y = -4/3x - 2/3

Then, manipulate the equation to get the answer:
multiply both side of the equation by 3.
3y = -4x + 2
4x + 3y -2 = 0

So, the answer is the fourth one.

Answer 5

Use the two points to find the slope of the line.

the slope formula is y sub2 - y sub1/ x sub2 - xsub1

(-6 - -2)/(4 - 1)

-6 + 2 = -4
4 - 1=3

Therefore, the slope is -4/3

Next, find the equation by using the y - y = m(x -x) formula

You can use either coordinate.

y - -6=-4/3 (x - 4)

y + 6= -4/3x + 16/3
y = -4/3x + 16/3 - 6
y = -4/3x + 16/3 -18/3
Multiply by three to eliminate the denominator

3y=-4x -2
Therefore, 4x + 3y + 2 = 0

Answer 6

You can test if a line goes through a point by putting in the values of x and y.

The point (1, -2) has x = 1, y=-2. Try out these values in the equation of the line:

4x - 3y - 2
= 4(1) - 3(-2) - 2
= 4 + 6 - 2

Is this equal to zero? No. So this point is not on the line. Try it in each of the equations in this way. Then try the second point.

Answer 7

You could just plug in each pair of points to each answer. Or you could solve by getting the slope (y2 - y1)/(x2 - x1)

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

and using the point-slope form of a line y - y1 = m(x - x1)

y - -2 = 4/3 (x - 1)

y + 2 = 4/3 (x - 1)

3y + 6 = 4(x - 1)= 4x - 4

and moving stuff to the same side to get 0

Answer 8

An equation for a line passing via (one million, 2) and (4, 6) is (y-y1)/(x-x1) = (y2-y1)/x2-x1) (y-2)/(x-one million) = (6-2)/(4-one million) = 4/3 y-2= 4/3(x-one million) y = 4/3x-4/3+2 = 4x/3-2/3 3y = 4x -2 4x-3y -2 = 0

Answer 9

Line passing through (1, -2) and (4, -6).

First off, calculate the slope. The slope formula is

m = (y2 - y1) / (x2 - x1). Now, plug in (1, -2) and (4, -6) for (x1, y1) and (x2, y2). This gives us

m = [-6 - (-2)] / [4 - 1]
m = -4/3

Now that we have our slope, we can obtain the equation of our line with the slope formula once again. This time, we're going to plug in (1, -2) and (x, y) for (x1, y1) and (x2, y2). That is,

(y2 - y1) / (x2 - x1) = m

But we now know the value of m. Therefore,

[y - (-2)] / [x - 1] = -4/3

And now we solve this.

(y + 2) / (x - 1) = -4/3

Cross multiplying,

3(y + 2) = -4(x - 1)
3y + 6 = -4x + 4

Moving everything to the left hand side,

4x + 3y + 2 = 0

Answer 10

General equation of line passing through two given points (x1,y1) and (x2,y2) is

(y-y1) / (y1-y2) = (x-x1) / (x1-x2).......

here let (x1,y1) = (1, -2)

(x2,y2) = (4, -6)

putting these values in general equation we get

(y - (-2)) / (-2 - (-6)) = (x-1) / (1- 4)

=> (y + 2 )/ (-2 + 6) = (x-1)/(-3)

=> ( y + 2)/ 4 = (x- 1 )/ -3

=> -3*(y + 2 ) = 4*(x-1 )

=> -3y - 6 = 4x - 4

=> 4x + 3y -4 + 6 = 0

=> 4x + 3y + 2 = 0

so 4x + 3y + 2 = 0 is the ANSWER .CHOICE NUMBER II matches.

Answer 11

first find your slope
(-2+6)/(1-4)
4/-3 is your slope
now plug in a point and solve for b
-2=4/-3+b
add 4/3 to each side
-2/3=b
write the equation
y=(-4/3)x-2/3
multiply the whole equation by 3
3y=-4x-2
add 4x and 2 to each side
4x+3y+2=0

Theres your answer