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

To find a linear equation for the line going through these two points we can use the point-slope formula.

However, first we need to determine the slope of the line.

The slope can be found by using the formula: #color(red)(m = (y_2 - y_1)/(x_2 - x_1)#
Where #m# is the slope and (#color(red)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points.

Substituting the two points given in the problem we can solve for #m# as:

#m = (-4 - 2)/(3 - (-1))#

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

#m = -3/2#

Now that we have the slope we can use the slope-point formula to write the equation for the line.

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))#
Where #color(red)(m)# is the slope and (#color(red)((x_1, y_1))#) is a point the line passes through.

Substituting the slope of #-3/2# and using the point #(-1, 2)# we can get the equation of the line as:

#y - 2 = -3/2(x - (-1))#

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

If we want this in the slope-intercept for we can solve for #y# as follows:

#y - 2 = -3/2x - (3/2 * 1)#

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

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

#y - 0 = -3/2x - 3/2 + 2#

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

#y = -3/2x - 3/2 + 2(2/2)#

#y = -3/2x - 3/2 + 4/2#

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