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?
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"If the momentum of an object increases by #20%#, what will be the percent increase in its kinetic energy?"
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
See a solution process below:
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)#
