What is the equation for the line passing through (4, 3) and parallel to 4x-5y=10

y = 4x/5 - 1/5

Step-by-step explanation:

Given an equation

4x - 5y = 10

First, find the slope m

Following this equation

y = mx + C

4x - 10 = 5y

To get y, divide through by 5

(4x - 10) / 5 = 5y/ 5

(4x - 10) / 5 = y

We can still separate

4x / 5 - 10/5 = y

4x/ 5 - 2 = y

Therefore, y = 4x/5 - 2

The slope m = 4/5

Using the equation of line

y - y_1 = m(x - x_1)

Provided with point ( 4 , 3)

x_1 = 4

y_1 = 3

Inserting those values into

y - y_1 = m(x - x_1)

y - 3 = m ( x - 4)

We've gotten m to be 4/5

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

open the bracket

y - 3 = 4x - 16 / 5

y = (4x - 16)/ 5 + 3/1

LCM is 5

y = (4x - 16 + 15) / 5

y = (4x - 1 )/ 5

We can separate it

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

Using y = mx + C

the equation of the line is

y = 4x/5 - 1/5