Find an equation of the line containing the given pair of points in point-slope form and in slope-intercept form. (1,5) and (3,6)

Question

asked Dec 23, 2021 194k views

1 Answer

Underdog · Answer 1 · 2021-12-27T19:10:33+0000

Answer:

Part 1)
y-5=(1)/(2)(x-1)

Part 2)
y=(1)/(2)x+(9)/(2) or
y=0.5x+4.5

Explanation:

we have

(1,5) and (3,6)

Find the slope

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

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

substitute

m=(6-5)/(3-1)

m=(1)/(2)

Part 1) Find the equation in point slope form

y-y1=m(x-x1)

we have

m=(1)/(2)

$point\ (1,5)$

substitute

y-5=(1)/(2)(x-1)

Part 2) Find the equation in slope-intercept form

y=mx+b

we have

y-5=(1)/(2)(x-1)

isolate the variable y

$y-5=(1)/(2)x-(1)/(2)\\\\y=(1)/(2)x-(1)/(2)+5\\\\y=(1)/(2)x+(9)/(2)$