Question

Would someone mind answering this for me? Thank you

Answer 1

(a) m =
`(1)/(2)`

calculate the slope (m) using the ' gradient formula '

m =
`\frac{(y_{2 - y_(1)) } }{(x_{2 - x _(1)) } }`

let (x₁, y₁) = (8, 9) and (x₂, y₂) = ( - 2, 4)

m =
`((4 - 9))/((-2 - 8))` =
`(-5)/(-10)` =
`(1)/(2)`

(b) y - 9 =
`(1)/(2)` (x - 8)

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

choose any of the 2 given points for (a, b) → (8, 9)

y - 9 =
`(1)/(2)` (x - 8) → " point- slope form"

(c) y =
`(1)/(2)` x + 5

the equation of a line in ' slope-intercept form ' is

y = mc + c

where m is the slope and c the y-intercept

expand and simplify the point- slope equation

y - 9 =
`(1)/(2)` x - 4

y =
`(1)/(2)` x - 4 + 9

y =
`(1)/(2)` x + 5 → " slope- intercept form"