How do you write an equation of a line given (-4,2), m=3/2?

2 Answers
Apr 7, 2017

Use the equation #y=mx+b#

the slope or #m# is already given therfore the equation now looks like,

#y=3/2x+b#

Solve for #b# by subbing point #P(-4,2)#

#2=3/2*(-4)+b#

#2=-6+b#

#b=8#

Therefore the equation of the line is,

#y=3/2x+8#

graph{3/2x+8 [-10, 10, -5, 5]}

Apr 7, 2017

See the entire solution process below:

Explanation:

We can use the point-slope formula to write an 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.

Substitute the slope and point from the problem gives:

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

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

We can also transform this equation to the slope-intercept form by solving for #y#. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

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

#y - color(red)(2) = 3/2x + 12/2#

#y - color(red)(2) = 3/2x + 6#

#y - color(red)(2) + 2 = 3/2x + 6 + 2#

#y - 0 = 3/2x + 8#

#y = color(red)(3/2)x + color(blue)(8)#