Question

2. A line goes through the points begin ordered pair 8 comma 9 end ordered pair and begin ordered pair negative 2 comma 4 end ordered pair. (a) What is the slope of the line? Show your work (b) Write the equation of the line in point-slope form. Show your work (c) Write the equation of the line in slope-intercept form. Show your work. Answer:

Answer 1

see explanation

Explanation:

(a)

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

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

substitute these values into the formula for m

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

(b)

the equation of a line in point- slope form is

y - b = m(x - a)

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

given 2 points on the line, we can use either to obtain the equation

using m =
`(1)/(2)` and (a, b ) = (8, 9 ) , then

y - 9 =
`(1)/(2)` (x - 8 ) ← equation in point- slope form

(c)

the equation of a line in slope- intercept form is

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

using the equation from part (b)

y - 9 =
`(1)/(2)` (x - 8) ← distribute parenthesis

y - 9 =
`(1)/(2)` x - 4 ( add 9 to both sides )

y =
`(1)/(2)` x + 5 ← equation in slope- intercept form