Question

Find the equation of a line through these two points (9,11) (21,27)

Answer 1

Answer:

1) The equation of the line in point slope form is equal to $y-11=\frac{4}{3}(x-9)$

2) The equation of the line in slope intercept form is equal to $y=\frac{4}{3}x-1$

3) The equation of the line in standard form is equal to $4x-3y=-3$

Step-by-step explanation:

we have that the line passes through the points

(9,11) and (21,27)

step 1

Find the slope

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

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{27-11}{21-9}$

$m=\frac{16}{12}$

$m=\frac{4}{3}$

step 2

Find the equation of the line into point slope form

The equation of the line is

$y-y1=m(x-x1)$

we have

$m=\frac{4}{3}$

$point (9,11)$

substitute

$y-11=\frac{4}{3}(x-9)$ -----> equation of the line into point slope form

step 3

Find the equation of the line in slope intercept form

$y=mx+b$

$y-11=\frac{4}{3}(x-9)$

$y=\frac{4}{3}x-12+11$

$y=\frac{4}{3}x-1$ -----> equation of the line in slope intercept form

step 4

Find the equation of the line in standard form

$Ax+By=C$

where

A is a positive integer

B and C are integers

$y=\frac{4}{3}x-1$

Multiply by 3 both sides to remove the fraction

$3y=4x-3$

$4x-3y=-3$ ----> equation of the line in standard form