Question

Write an equation of the line passing through each of the following pairs of points.

(5, 7), (−8, −4)

Answer 1

y= 11/13x + 36/13

Explanation:

y=mx+b

y2 -y1 -4-7 = -11

x1-x2 -8-5= -13

slope is 11/13

Answer 2

y =
`(11)/(13)` x +
`(36)/(13)`

Explanation:

First, find the slope of the line passing through the points

Then find the y-intercept of the line

Then construct the formula

1. find the slope

remember the formula

`(y_(2) -y_(1) )/(x_(2) -x_(1) )` is used to find the slope

now plug in the given points

(5, 7)

(-8, -4)

`x_(1) = 5\\y_(1) = 7\\x_(2) = -8 \\y_(2) = -4`

`((-4) - (7))/((-8) - (5))`

simplify and solve

=
`(-11)/(-13)`

=
`(11)/(13)`

2. find the y-intercept

remember the base formula for a line

y= mx + b

where m is the slope and b is the y-intercept

we know the slope, so now plug in one of the given coordinates for a point on the line and slove to find the y-intercept

y = mx + b

y =
`(11)/(13)`x + b

use the first set of given coordinates for a point on this line: (5, 7)

7 =
`(11)/(13)` * 5 + b

solve by inverse operations and simplifying

7 =
`(55)/(13)` + b

`(36)/(13)` = b

3. construct the formula

now we know the slope and the y-intercept, all we have to do now is substitute it into the base formula for a line:

y = mx + b

where m is the slope and B is the y-intercept

we found that

m =
`(11)/(13)`

and

b =
`(36)/(13)`

so that means the equation is

y =
`(11)/(13)` * x +
`(36)/(13)`