Home > Algebra > Write an Equation Given Two Points

How do you write the standard form of a line given (3, 4) and (–3, –8)?

Answer 1

Julia Adams

#y=2x-2#

Find the gradient before attempting to find the equation of a line.

For co-ordinates #(x_1, y_1)# and #(x_2, y_2)#, define #"grad" as (y_2-y_1)/(x_2-x_1)#.

#"grad" = (8-4) / (3-3)#

#=(-12)/(-6)#

#=2#

The following is the formula for a line with gradient m through #(x_1, y_1)#:

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

#y-4=2(x-3)#

#y-4=2x-6#

#y=2x-2#

graph{y=2x-2 [-11.24, -1.24, 7.835, -12.165]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nathan Axel

To write the standard form of a line given two points, you first find the slope using the formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ), where ( (x_1, y_1) ) and ( (x_2, y_2) ) are the coordinates of the two points. Once you have the slope ( m ), you can use one of the points and the slope in the point-slope form ( y - y_1 = m(x - x_1) ). Finally, you can rearrange the equation into standard form ( Ax + By = C ), where ( A ), ( B ), and ( C ) are integers and ( A ) is positive.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.