How do you find an equation of the line having the given slope and containing the given point m=-8, (4,5)?

1 Answer
Jan 3, 2017

Use the slope-point formula to complete this question. See full explanation below.

Explanation:

Because we have been given a slope and a point on the line we can use the point-slope formula to complete this problem.

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 information we are provided gives us this equation:

#(y - color(red)(5)) = color(blue)(-8)(x - color(red)(4))#

If we want to put this in the more familiar form of the slope-intercept form we can solve for #y# as follows:

#y - color(red)(5) = color(blue)(-8)x - (color(blue)(-8) xx color(red)(4)))#

#y - color(red)(5) = color(blue)(-8)x - (-32)#

#y - color(red)(5) = color(blue)(-8)x + 32#

#y - color(red)(5) + 5 = color(blue)(-8)x + 32 + 5#

#y - 0 = color(blue)(-8)x + 37#

#y = -8x + 37#