Write an equation in standard form for a line passing through A(-2, 3) and B(3,4)

Question

The answer I got was x-y=1; is this correct?

Answer 1

Hi, Rachel!

 

First, you need to know... what is the standard form of an equation? Since this is a linear equation (we can see this because it passes through 2 points), the standard form will be Ax + By = C.

 

Now, most students remember the slope intercept form, y = mx +b, where m is the slope and b is the point where the line goes through the y-axis. Careful here, that little "b" is not the same as the capital "B". Now we can use the two points you are given to find the slope using the formula

 

(y2-y1)/(x2-x1)          

 

It doesn't really matter which point you use for (x1, y1) or (x2,y2), so    (4-3)/(3--2)   or    (3-4)/(-2-3)

should both give you a slope of 1/5

 

Now we have y = (1/5)x + b.  Take one of your two points and throw it in for x and y. Example: 4 = (1/5)3 + b

Once you solve for b, return the x and y to the equation and rearrange the terms to the standard form. It should look like 

 

- 0.2x + y = 3.4      (Notice I switched to decimals!... cuz who likes fractions??  Maybe that's a different lesson.)

 

 

 

 

 

Answer 2

Rachel, does -2 - 3 = 1?  No.  Does 3 - 4 = 1? No.

 

First, you need to find the slope, m = (y₂ - y₁)/(x_{2 -} x₁).  Slope intercept form is y = mx + b.  Pick a point and place the x and y into this equation with your slope.  Solve it for b.

 

Now you should have m and b.  Place them into y = mx + b and convert to standard form.

 

Hope this helps.