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

Question

Isaiah Anthony · Accepted Answer

See full solution process below.

First, we can use the point-slope formula to get the equation for this line since we know the slope and point: 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. When the problem's slope and point are substituted, the following happens: #(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#

Savannah Anderson · Answer

undefined To find the value of $ a $, you can use the point-slope form of the equation of a line:

$$ y - y_1 = m(x - x_1) $$

where $ (x_1, y_1) $ is a point on the line and $ m $ is the slope.

Given that the line contains point $ P(3,4) $ and has a slope of $ -2 $, you can plug these values into the point-slope form:

$$ y - 4 = -2(x - 3) $$

Now, substitute the x-coordinate of point $ Q $ into the equation and solve for $ y $ to find the value of $ a $:

$$ y - 4 = -2(-4 - 3) $$
$$ y - 4 = -2(-7) $$
$$ y - 4 = 14 $$
$$ y = 14 + 4 $$
$$ y = 18 $$

So, the value of $ a $ is $ 18 $.