How do you write an equation of a line passing through (4,8) and (1,2)?

We can use the point-slope formula to write the equation of a line passing through these two points. First, however, we must determine 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 values from the points in the problem gives:

#m = (color(red)(2) - color(blue)(8))/(color(red)(1) - color(blue)(4))#

#m = (-6)/(-3)#

#m = 2#

Now we can use the slope and the first point in the point-slope formula to find an equation.

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.

#(y - color(red)(8)) = color(blue)(2)(x - color(red)(4))#

We can also use the slope and the second point in the point-slope formula to find an equation.

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