# Thread: analytic geometry question

2. ## Re: analytic geometry question

Originally Posted by Mhmh96
One general way: the equation of the straight line passing trough the the points $(x_1,y_1)$ and $(x_2,y_2)$ is $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Particular way: is horizontal our straight line?

3. ## Re: analytic geometry question

I think b refer to the y-axis ,right?

4. ## Re: analytic geometry question

Originally Posted by Mhmh96
I think b refer to the y-axis ,right?
Right, so $m=\ldots ?\;,\quad b=\ldots ?$

5. ## Re: analytic geometry question

Now how can i find the slope of this line? ,do i need just apply the law of finding the slope of line like this...-7+7/1+2=0/3=0 ?

6. ## Re: analytic geometry question

Originally Posted by Mhmh96
Now how can i find the slope of this line? ,do i need just apply the law of finding the slope of line like this...-7+7/1+2=0/3=0 ?
Yes, that's the correct method (and 0 is the correct answer).

One small remark though: $-7+7/1+2$ is not the correct the way to write your calculation. This calculation is solved as:
$-7+7/1+2=-7+7+2=2$
which I think is not what you meant.

The correct way of writing is with either brackets or fractions, like this:
$(-7+7)/(1+2)$ or $\frac{-7+7}{1+2}$

7. ## Re: analytic geometry question

Another way: you want y= mx+ b and both (x, y)= (-2, -7) and (x, y)= (1, -7) must satisfy that equation. Putting those values into the equation, we have -7= m(-2)+ b and -7= m(-1)+ b so can solve the simultaneous equations -2m+ b= -7, -m+ b= -7.

Of course, the easiest way to solve this particular problem is to observe that both points have y-value -7. Since a straight line is determined by two points, that's a horizontal line and y= -7 must be the equation.