Equation of a line

Question

What is the equation of the line that passes through the points (-1,3) and (0,1)?

Answer 1

Since the line passes through points  (-1,3) and (0,1), we can calculate the slope by using the formular

 

slope= (y₂-y1_{)/ (}x_2-x_1).

 

_{Here we can let  y2 = 3,  x2=-1 (the first point); y1=1, x1=0 (the second point).  So the slope =(y2-y1)/ (x2-x1) = (3-1)/(-1-0) = 2/(-1) = - 2.}  

 

OR we can let  y2 = 1 x2=0 (the second point);  y1=3, x1=-1 ( the first point), and get the same slope by suing the formular slope =(y2-y1)/ (x2-x1) = (1-3)/[0-(-1)]= -2/1 =-2

 

Finally, we apply the slope intercept form: (y-y₀₎₌slope *(x-x₀).  We can pick either of the two points as (x_0, y_0).

 

1) (x0, y0) = (-1, 3)

y-3=-2*[x-(-1)]

y-3 = -2x - 2

y = -2x +1

 

2) (x0, y0) = (0,1)

Then y-1=-2(x-0)

 We can get y = -2x+1 as well.

 

Hope this helps.

 

 

 

 

Answer 2

Hi Shonna,

 

The general equation for a line is y = mx +b where m is the slope and b is the y intercept (the point on the y axis where the line passes through).

 

Your first step is to figure the slope which is the change in y divided by the change in x.

 

3 and 1 are the y's

 

-1 and 0 are the x's

 

So (3-1) / (-1 - 0) = m

m - 2/-1 = -2

 

Now to figure out b, you plug in one of the points into the equation.  Let's choose the point with zero in it because the math is probably easier:

 

y = mx + b

1 = (-2) (0) + b

1 = 0 +b

b = 1

 

So the equation for the line is y = -2x + 1

 

Plug in (-1,  3) into the equation to see if it works.

 

Have fun.

 

Dan

Answer 3

Hi! If you use the slope-intercept form, you will need to know the slope of the line and the y-intercept. One of the points is on the y axis (0,1), giving you the intercept. Therefore you only need to calculate the slope. Recall that slope is rise over run (change in y divided by change in x). Your y-values go from 3 to 1, so the change is 3-1 or 2.

The change in x is from -1 to 0 or -1-0, which is -1.

 

The slope is 2/-1, or -2.

 

Therefore the equation of the line is y=-2x+1

 

Hope this helps

 

Mike

Answer 4

Hi there. I took the graphic approach. If you draw up Point A (-1,3) and Point B (0,1) on a graph, you go down 2 and over 1 from A to B. If you take slope to be rise over run, or change in y/change in x, this results in -2/1 or a -2 slope. To finish the equation, we need to figure out where this line intercepts the y-axis. You are conveniently given Point B (0,1), which in fact is on the y-axis already. So the line intercepts at +1 on the y-axis at this point. So the expression of a line is (rise/run)x + the y intercept (y = mx+b), we have y = -2x + 1.

 

Hope that helps!