Question

Help and hurry plzzzzzzzzzzzzz

Answer 1

The equation of the line in the slope-intercept form is y =
`(4)/(3)` x + 4 ⇒ A

Explanation:

The slope-intercept form is y = m x + b, where

• m is the slope of the line
• b is the y-intercept (y at x = 0)

The formula of the slope of a line which passes through points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

∵ The line passes through points (-6 , -4) and (0 , 4)

∴
`x_(1)` = -6 and
`x_(2)` = 0

∴
`y_(1)` = -4 and
`y_(2)` = 4

- Substitute them in the formula of the slope

∴
`m=(4--4)/(0--6)=(8)/(6)`

- Simplify it by divide up and down by 2

∴
`m=(4)/(3)`

∵ The slope-intercept form is y = m x + b

- Substitute the value of m on it

∴ y =
`(4)/(3)` x + b

∵ b is value y at x= 0

∵ At x = 0 , y = 4 ⇒ given point

∴ b = 4

- Substitute the value of b in the equation

∴ y =
`(4)/(3)` x + 4

The equation of the line in the slope-intercept form is y =
`(4)/(3)` x + 4