How do you write an equation of a line given (-1, 2) and (3, -4)?

Question

Eli Assouline · Accepted Answer

#3x+2y+1=0# Standard form of equation with two points given is #(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)# #(y-(-4))/(2-(-4))=(x-3)/(-1-3)# #(y+4)/6=(x-3)/(-4)# #-4y-16= 6x - 18# #6x+4y=2# #3x+2y=1#

Ethan Adkins · Answer

#y=-3/2x+1/2#

Okay so there are 3 main forms you can use: - slope-intercept form [#y=mx+b#] - standard form [#Ax+By=C#] - point-slope form [#y_1-y_2=m(x_1-x_2)#]

Since you did not specify which form you wanted it in, I am going to use slope-intercept form because that's the easiest to understand, in my opinion. (:

#y=mx+b#

SLOPE (#m#) To find #m# (slope), you need to find #(rise)/(run)#, or which is the change in #y# divided by the change in #x#. Use this formula: #(y_1-y_2)/(x_1-x_2)# #(-1, 2) = (x_1, y_1)# #(3, -4) = (x_2, y_2)#

It doesn't matter which coordinate pair you choose to be #(x_1, y_1)# or #(x_2, y_2)#. Just stay consistent!

#m = [2-(-4)]/[-1-3] = (2+4)/(-1-3) = 6/-4 = -3/2# #m#= -3/2#

Y-INTERCEPT (#b#) Choose one of the coordinates to substitute into #y=mx+b#, which will be substituting for #x# and #y#. I chose #(-1, 2)#. Substitute #m# for #-3/2#. #(2)=(-3/2)(-1)+b# Solve for #b#. #2=3/2+b# #b=1/2#

FINAL FORM Substitute #m# and #b# for their values. This is your answer! #y=-3/2x+1/2#

Jameson Allen · Answer

undefined To write the equation of a line given two points (-1, 2) and (3, -4), you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line, and m is the slope of the line. First, calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, 2) and (x2, y2) = (3, -4). Then, substitute the values into the formula to find the equation of the line.