How do you write an equation in standard form given that the line passes through (-1, -3) and (2, 1)?

Question

Julia Adams · Accepted Answer

Using this formula with the given points:
#(x-x_0)/(x_1-x_0)=(y-y_0)/(y_1-y_0)#  The points are: So the equation of the line passing through A and B becomes:
#(x-(-1))/(2-(-1))=(y-(-3))/(1-(-3))#  #(x+1)/(2+1)=(y+3)/(4)#  #(x+1)/3=(y+3)/(4)#  Now we must bring the equation in a "standard form" that means an equation similar to #ax+by+c=0# #4*(x+1)=(y+3)*3#  # 4x +4 = 3y + 9 # #4x-3y-5=0# graph{4x-3y-5=0 [-3, 3,-3,3]}

Abigail Allen · Answer

undefined To write an equation in standard form given that the line passes through (-1, -3) and (2, 1), follow these steps:

1. Determine the slope using the formula: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $
2. Substitute the coordinates of one point and the slope into the point-slope form equation: $ y - y_1 = m(x - x_1) $
3. Rewrite the equation in slope-intercept form: $ y = mx + b $
4. Solve for $ b $ using the coordinates of either point.
5. Rewrite the equation with $ m $ and $ b $.
6. Rewrite the equation in standard form: $ Ax + By = C $, where $ A $, $ B $, and $ C $ are integers.

So, the equation in standard form would be: $ 3x - 3y = 12 $.