Question

Help me with is problem

Answer 1

y-intercept = (0, - 2) and x-intercept = (
`(3)/(2)`, 0)

the equation of a line in slope-intercept form is

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

The 3 given points all lie on the same line

calculate m using the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (6, 10)

m =
`(10-6)/(6-3)` =
`(4)/(3)`

partial equation is y =
`(4)/(3)` x + c

to find c substitute any of the 3 points into the partial equation

using (3, 6 ), then

6 = 8 + c ⇒ = 6 - 8 = - 2 ⇒ (0, - 2 )← y-intercept

y=
`(4)/(3)` x - 2 ← equation of line

To find the x-intercept, let y = 0, in the equation and solve for x

`(4)/(3)` - 2 = 0 ( add 2 to both sides )

`(4)/(3)` x = 2 ( multiply by 3 and divide by 4 )

x =
`(3)/(2)` ⇒ (
`(3)/(2)`, 0) ← x-intercept