PLEASE HELP!! Find the equation of the line that passes through (1,5) and (2,8).
Find the equation of the line that passes through (-2,-7) and (4,-10).

1. y=3x+2

2. y=-1/2x-8

Step-by-step explanation:

1.  Find the equation of the line that passes through (1,5) and (2,8).

slope-intercept form of the line is y=mx+b

the given points are (1,5) and (2,8)

the equation for slope (m) is (y2-y1)/(x2-x1)

label the points:

x1=1

y1=5

x2=2

y2=8

substitute into the equation

m=(8-5)/(2-1)

m=3/1

m=3

the slope is 3

use slope-point form, which is y-y1=m(x-x1)

once again, substitute into the equation:

y-5=3(x-1)

do distributive property

y-5=3x-3

add 5 to both sides

y=3x+2

the equation of the first line is y=3x+2

2. Find the equation of the line that passes through (-2,-7) and (4,-10).

we are given the points (-2,-7) and (4,-10)

label the points:

x1=-2

y1=-7

x2=4

y2=-10

substitute into the equation for slope:

m=(-10--7)/(4--2)

m=(-3)/6

m=-1/2

the slope is -1/2

use slope-point form again:

y--7=-1/2(x--2)

y+7=-1/2(x+2)

do distributive property

y+7=-1/2x-1

subtract 7

y=-1/2x-8

the second equation is y=-1/2x-8

hope this helps :D

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4