How do you write the equation of the line between the points (2, 4) and (-2,8)?

We can use the point-slope formula to write this equation.

However, first we must find the slope.

The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the two points from the problem gives:

#m = (color(red)(8) - color(blue)(4))/(color(red)(-2) - color(blue)(2))#

#m = 4/-4#

#m = -1#

Now we can use the point slope formula.

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope we calculate and one of the points gives:

#(y - color(red)(4)) = color(blue)(-1)(x - color(red)(2))#

Putting this in the more familiar slope-intercept form by solving for #y# gives:

#y - color(red)(4) = color(blue)(-1)x - (color(blue)(-1) xx color(red)(2))#

#y - color(red)(4) = color(blue)(-1)x - (-2)#

#y - color(red)(4) = color(blue)(-1)x + 2#

#y - color(red)(4) + 4 = color(blue)(-1)x + 2 + 4#

#y - 0 = color(blue)(-1)x + 6#

#y = -x + 6#

You can find the line by the following formula:

#(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#

where #(x_1;y_1)# and #(x_2;y_2)# are the given points.

Then the line is:

#(y-4)/(8-4)=(x-2)/(-2-2)#

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

#y-4=-x+2#

#x+y-6=0#