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What is the equation in point-slope form and slope intercept form for the line given (9, 1) and (4, 16)?

Answer 1

Eli Assouline

The point-slope form is #y-1=-3(x-9)#, and the slope-intercept form is #y=-3x+28#.

Determine the slope, #m#, using the two points.

Point 1: #(9,1)# Point 2: #(4,16)#

#m=(y_2-y_1)/(x_2-x_1)=(16-1)/(4-9)=(15)/(-5)=-3#

Point-slope form.

General equation: #y-y_1=m(x-x_1)#, where #x_1# and #y_1# are one point on the line. I will use Point 1: #(9,1)#.

#y-1=-3(x-9)#

Slope-intercept form.

General equation: #y=mx+b#, where #m# is the slope and #b# is the y-intercept.

Solve the point-slope equation for #y#.

#y-1=-3(x-9)#

Distribute the #-3#.

#y-1=-3x+27#

Add #1# to each side.

#y=-3x+28#

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Answer 2

Jameson Allen

Point-slope form: y - 1 = -3(x - 9) Slope-intercept form: y = -3x + 28

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.