A line has slope -2 and contains P(3,4) and Q(-4, a). How do you find the value of a?

1 Answer
Jan 9, 2017

See full solution process below.

Explanation:

First, because there is a slope and point given we can use the point-slope formula to obtain the equation for this line:

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 and point from the problem results in:

#(y - color(red)(4)) = color(blue)(-2)(x - color(red)(3))#

We can now convert this to more familiar slope-intercept form by solving the equation for #y#:

#y - color(red)(4) = color(blue)(-2)x + (color(blue)(2) xx color(red)(3))#

#y - color(red)(4) = color(blue)(-2)x + 6#

#y - color(red)(4) + 4 = color(blue)(-2)x + 6 + 4#

#y - 0 = color(blue)(-2)x + 10#

#y = -2x + 10#

To find #a# we can substitute #-4# for #x# and #a# for #y# and calculate #a#:

#a = (-2 xx -4) + 10#

#a = 8 + 10#

#a = 18#