# Thread: Finding the equation of a line from two given points.

1. ## Finding the equation of a line from two given points.

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 + _____).

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

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

4. 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?

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

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

7. i got the first problem already but need second problem

8. 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 $\displaystyle -\frac{4}{3}$.

9. thank u so much.

10. 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:

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

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

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

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

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

2 is the answer you need.

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

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