What is the slope intercept form of the line passing through #(-10,6) # with a slope of #3/2 #?

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Answer 1 · 2017-08-28T14:09:12

See a solution process below:

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 substitute the slope from the problem to give:

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

Into the equation we can now substitute the values from the point for #x# and #y# and then solve for #color(blue)(b)#

#6 = (color(red)(3/2) xx -10) + color(blue)(b)#

#6 = -color(red)(30/2) + color(blue)(b)#

#6 = -color(red)(15) + color(blue)(b)#

#15 + 6 = 15 - color(red)(15) + color(blue)(b)#

#21 = 0 + color(blue)(b)#

#21 = color(blue)(b)#

We can now substitute this along with the into the formula to give:

#y = color(red)(3/2)x + color(blue)(21)#