How do you write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

2 Answers
Jun 1, 2018

Point-Slope Form is
#y+3 = 1/2(x-6)#

Slope-Intercept Form is
#y = 1/2x-6#

Explanation:

The point-slope form of the equation of a line is

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

Where #m# is the slope and the point is #(x_1,y_1)#

For this problem

#m=1/2#
#x_1 = 6#
#y_1=-3#

Plug in the values

#y-(-3) = 1/2(x-6)#

Simplify the signs

#y+3 = 1/2(x-6)#
This is the point-slope form of the equation

Now solve for #y# to get the slope-intercept form.

#y+3 = 1/2(x-6)#

Use the distributive property to eliminate the parenthesis

#y+3 = 1/2x-3#

Now isolate the #y# using the additive inverse

#y cancel(+3) cancel(-3) = 1/2x-3-3#

#y = 1/2x-6#
This is the slope-intercept form of the equation

Jun 1, 2018

See a solution process below:

Explanation:

The point-slope form of a linear equation is:

#(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#

Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope

Substituting the slope and values from the point in the problem gives:

#(y - color(blue)(-3)) = color(red)(1/2)(x - color(blue)(6))#

#(y + color(blue)(3)) = color(red)(1/2)(x - color(blue)(6))#

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.

We can solve the point-slope equation for #y# giving:

#(y + color(blue)(3)) = color(red)(1/2)(x - color(blue)(6))#

#y + color(blue)(3) = (color(red)(1/2) xx x) - (color(red)(1/2) xx color(blue)(6))#

#y + color(blue)(3) = 1/2x - 6/2#

#y + color(blue)(3) = 1/2x - 3#

#y + color(blue)(3) - color(blue)(3) = 1/2x - 3 - color(blue)(3)#

#y + 0 = 1/2x - 6#

#y = color(red)(1/2)x - color(blue)(6)#