Question

A line goes through the points (8,9) and (-2,4)

(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 1

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

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

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

Explanation:

(a) slope of line passing through two points
`(x_1,y_1)` and
`(x_(2),y_(2))` is given by

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

Here
`(x_(1),y_(1))=(8,\ 9),\ (x_(2),y_(2))=(-2,\ 4)`

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

Slope
`=(1)/(2)`

Equation in point slope form

Equation of line passing through a point
`(x_(1),\ y_(1))` and having slope
`m` is given by
`(y-y_(1))=m(x-\ x_(1))`

Here
`(x_(1),y_(1))=(8,9}), \ m=(1)/(2)`

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

slope intercept form

Equation is given by
`y=m\ x+b`

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

`y=(x)/(2)+b`

it passes through
`(8,9)`

`9=(8)/(2)+b\\9=4+b\\b=5`

Hence equation is
`y=(x)/(2)+5`