Question

Identify an equation in point-slope form for the line parallel to y=-(2)/(3)x+8 that passes through (4,-5).

Answer 1

Hello :)

`\underline{\sf{Answer:}}`

y + 5 = -2/3(x - 4)

`\underline{\sf{Step-by-step\;explanation:}}`

Our task is to identify an equation in point-slope form for the line parallel to
`\rm{y=-\cfrac{2}{3}x+8}` that passes through (4,-5).

Parallel lines have the same slope, so the slope (m) is -2/3.

Point-slope is:
`\rm{y-y_1=m(x-x_1)}`.

Replace y_1 with -5:

`\rm{y-(-5)=m(x-x_1)}`

`\rm{y+5=m(x-x_1)}`

Replace m with -2/3 and x_1 with 4:

`\boxed{\rm{y+5=-\cfrac{2}{3}(x-4)}}`

Answer 2

y + 5 = -
`(2)/(3)` (x - 4)

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = -
`(2)/(3)` x + 8 ← is in slope- intercept form

with slope m = -
`(2)/(3)`

• Parallel lines have equal slopes

then slope of parallel line m = -
`(2)/(3)`

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = -
`(2)/(3)` and (a, b ) = (4, - 5 ) , then

y - (- 5) = -
`(2)/(3)`(x - 4) , that is

y + 5 = -
`(2)/(3)` (x - 4) ← in point- slope form