Question

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

Answer 1

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`