How do you write an equation in standard form given point (1,-1) and (3,5)?

Question

Eva Abramson · Accepted Answer

Standard form is #ax+by=c# but you are only given 2 points so you cannot write 3 equations to solve for, a, b, and c. You must use the points to find the slope and then convert the point-slope form.

Use the two points to find the slope: #m = (y_1-y_0)/(x_1-x_0)# #m = (5 - -1)/(3-1)# #m = 6/2# #m = 3# Use the point-slope form for the equation of a line: #y=m(x-x_1)+y_1# #y=3(x-3) + 5# Now convert to standard form: #y = 3x-9+5# #y = 3x-4# #3x-y=4" "larr# standard form

Ethan Adkins · Answer

undefined To write an equation in standard form given two points (1, -1) and (3, 5), you first find the slope using the formula:

$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $

Next, choose one of the points and use the slope to find the equation of the line in point-slope form:

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

Then, rewrite the equation in slope-intercept form $ y = mx + b $ and manipulate it into standard form $ Ax + By = C $ by moving all terms to one side of the equation and ensuring that the coefficients $ A $ and $ B $ are integers and $ A $ is positive.