Question

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

Answer 1

Answer:

y= 11/13x + 36/13

Step-by-step explanation:

y=mx+b

y2 -y1         -4-7 = -11

x1-x2           -8-5= -13

slope is 11/13

Answer 2

Answer:

y = $\frac{11}{13}$ x + $\frac{36}{13}$

Step-by-step 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

$\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$ is used to find the slope

now plug in the given points

(5, 7)

(-8, -4)

$x_{1} = 5\\y_{1} = 7\\x_{2} = -8 \\y_{2} = -4$

$\frac{(-4) - (7)}{(-8) - (5)}$

simplify and solve

= $\frac{-11}{-13}$

= $\frac{11}{13}$

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 = $\frac{11}{13}$x + b

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

7 = $\frac{11}{13}$  * 5 + b

solve by inverse operations and simplifying

7 = $\frac{55}{13}$ + b

$\frac{36}{13}$ = 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 = $\frac{11}{13}$

and

b = $\frac{36}{13}$

so that means the equation is

y = $\frac{11}{13}$ * x + $\frac{36}{13}$