Question

find the equation of the line passing through the given points. write the equation in slope-intercept form (1/5,-4) and (16/5,-9)

Answer 1

Answer:

$y=-\frac{5}{3}x-\frac{11}{3}$

Step-by-step explanation:

We need to write the equation in slope-intercept form which passes through points (1/5,-4) and (16/5,-9)

Slope is given formula:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-9-\left(-4\right)}{\frac{16}{5}-\frac{1}{5}}=\frac{-9+4}{\frac{15}{5}}=\frac{-5}{3}$

Now plug the value of slope m and any one of the given point into point slope formula:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-4\right)=\frac{-5}{3}\left(x-\frac{1}{5}\right)$

$y+4=-\frac{5}{3}x+\frac{1}{3}$

$y=-\frac{5}{3}x+\frac{1}{3}-4$

Now simplify this and write in slope intercept form y=mx=b

$y=-\frac{5}{3}x-\frac{11}{3}$

Hence final answer is $y=-\frac{5}{3}x-\frac{11}{3}$

Answer 2

Answer:

y=$\frac{-5}{3}$x$\frac{-11}{3}$

Step-by-step explanation:

y'-y1=m(x-x1)...........(1)

given

(x1,y1)=($\frac{1}{5}$,-4)

(x2,y2)=($\frac{16}{5}$,-9)

we know that slope=m=($\frac{y2-y1}{x2-x1}$)

put values of (x1,y1) and (x2,y2)in above formula

we get

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

m=($\frac{-9-(-4)}{16/5-1/5}$)

m=($\frac{-9-+4)}{15/5}$)

m=($\frac{-5)}{15/5}$)

m=($\frac{-5)}{3}$)

now put slope (m) and points (x1,y1) in (1)

y-y1=m(x-x1)

y-(-4)=-5/3(x-1/5)

y+4= (-5/3)x+1/3

finally we get

y=$\frac{'-5}{3}$x+$\frac{1}{3}$-4

y=$\frac{-5}{3}$x$\frac{-11}{3}$