Finding the equation of a line from two given points.

**daniel323** · May 6th 2010, 11:29 AM

plz neeed help with this If a line passes through the points (-2, -4) and (3, -1), the equation of the line is y + 4 = 3/5(x + _____).

**mohammadfawaz** · May 6th 2010, 11:33 AM

First find the equation of the line as $y=mx+b$ . You know how do this right?
Now, $y+4=mx+b+4$ from which you should be able to factor $\frac{3}{5}$ .

**daniel323** · May 6th 2010, 11:40 AM

i dont know how to do this so 3/5 is the answer

**undefined** · May 6th 2010, 11:47 AM

Originally Posted by daniel323

i dont know how to do this so 3/5 is the answer

This question is supposed to be testing your understanding of and ability to recognize the point-slope equation.

Do you see it?

**daniel323** · May 6th 2010, 11:47 AM

can u help with this problem also Yfrog Image : yfrog.com/j9math14p

**mohammadfawaz** · May 6th 2010, 11:48 AM

Ok, first, the equation of the line should be of the form $y=mx+b$ where m is slope and given by $m=\frac{y_2-y_1}{x_2-x_1} = \frac{-1-(-4)}{3-(-2)} = \frac{3}{5}$ .
Hence, $y=\frac{3}{5}x+b$ . Still need to find b.
the point (-2,-4) belongs to the lines, hence: $-4=\frac{3}{5}\times (-2)+b$ , therefore: $b = -4+\frac{6}{4} = -4+\frac{3}{2}$ .
Hence, $y=\frac{3}{5}x-4+\frac{3}{2}$ .
So, $y+4=\frac{3}{5}x+\frac{3}{2} = \frac{3}{5}(x+\frac{3/2}{3/5}) = \frac{3}{5}(x+\frac{5}{2})$ .
$\frac{5}{2}$ is the answer you need.

**daniel323** · May 6th 2010, 11:50 AM

i got the first problem already but need second problem

**mohammadfawaz** · May 6th 2010, 11:50 AM

For the second question, it is clear from the figure that the two lines are parallel. This means that they have the same slope, hence your answer is $-\frac{4}{3}$ .

**daniel323** · May 6th 2010, 11:53 AM

thank u so much.

**masters** · May 6th 2010, 11:54 AM

Originally Posted by daniel323

plz neeed help with this If a line passes through the points (-2, -4) and (3, -1), the equation of the line is y + 4 = 3/5(x + _____).

Hi daniel323,

Are you familiar with the 'point-slope' form of a linear equation:

$y-y_1=m(x-x_1)$

Find your slope, which is already given to you as $\frac{3}{5}$

Use (-2, -4) as $(x_1, y_1)$ and the equation:

$y-y_1=m(x-x_1)$

And fill in the blank: $y-(-4)=\frac{3}{5}(x-(-2))\Longrightarrow \boxed{y+4=\frac{3}{5}(x+{\color{red}2})}$

2 is the answer you need.

**undefined** · May 6th 2010, 11:56 AM

Originally Posted by mohammadfawaz

Ok, first, the equation of the line should be of the form $y=mx+b$ where m is slope and given by $m=\frac{y_2-y_1}{x_2-x_1} = \frac{-1-(-4)}{3-(-2)} = \frac{3}{5}$ .
Hence, $y=\frac{3}{5}x+b$ . Still need to find b.
the point (-2,-4) belongs to the lines, hence: $-4=\frac{3}{5}\times (-2)+b$ , therefore: $b = -4+\frac{6}{4} = -4+\frac{3}{2}$ .
Hence, $y=\frac{3}{5}x-4+\frac{3}{2}$ .
So, $y+4=\frac{3}{5}x+\frac{3}{2} = \frac{3}{5}(x+\frac{3/2}{3/5}) = \frac{3}{5}(x+\frac{5}{2})$ .
$\frac{5}{2}$ is the answer you need.

I know the OP said this problem is already solved, but I'd just like to point out that there is an error here, there was a (6/4) where there should have been a (6/5), and the value for b is wrong.

Using point-slope equation, once you verify that the slope is (3/5), you can immediately see that the answer is 2.

Edit: Ah, masters beat me to it.

**mohammadfawaz** · May 6th 2010, 11:59 AM

Oh!
sorry for that!
I had a typing mistake that got me all wrong,
So, 2 is the correct answer

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