What is the slope-intercept form of the line passing through # (5, 1)# and # (3, -2) #?

1 Answer
Tony B
Jun 30, 2016

#y=3/2x-13/2#

Explanation:

Slope intercept form is:#" "y=mx+c#
where #m# is the gradient and #c# is the y-intercept.

Gradient#->("change in y")/("change in x")#

Let point 1 be #P_1->(x_1,y_1)=(5,1)#
Let point 2 be #P_2->(x_2,y_2)=(3,-2)#

Thus Gradient #->(y_2-y_1)/(x_2-x_1)= (-2-1)/(3-5) =(-3)/(-2)=+3/2#
'.......................................................................................................
So now we have #y=3/2x+c#

To find the value of #c# we substitute in the value of a known point so that there is only 1 unknown.

#color(brown)(=>P_1->y_1=3/2x_1+c)color(blue)( -> 1=3/2(5)+c)#

#" "1=15/2+c#

Subtract #color(magenta)(15/2)# from both sides

#" "color(blue)(1color(magenta)(-15/2)=15/2 color(magenta)(-15/2)+c#

#c=-13/2#
'.........................................................................................................

#" "bar(ul(|color(white)(.)y=3/2x-13/2color(white)(.)|))#

Tony B

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