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3. A line goes through the points (3,4) and (-3,6).

(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.

User Singletony
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1 Answer

3 votes

Answer:

Part a) The slope is
m=-(1)/(3)

Part b) The equation in point slope form is
y-4=-(1)/(3)(x-3)

Part c) The equation in slope-intercept form is
y=-(1)/(3)x+5

Explanation:

we have the points (3,4) and (-3,6)

Part a) What is the slope of the line?

The formula to calculate the slope between two points is equal to


m=(y2-y1)/(x2-x1)

substitute the given points


m=(6-4)/(-3-3)


m=(2)/(-6)


m=-(1)/(3)

Part b) Write the equation of the line in point-slope form


y-y1=m(x-x1)

we have


m=-(1)/(3)


point\ (3,4)

substitute


y-4=-(1)/(3)(x-3) ---> equation in point slope form

Part c) Write the equation of the line in slope-intercept form


y=mx+b

we have


y-4=-(1)/(3)(x-3)

Isolate the variable y

distribute right side


y-4=-(1)/(3)x+1

Adds 4 both sides


y=-(1)/(3)x+1+4


y=-(1)/(3)x+5 ---> equation in slope intercept form

User Codist
by
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