Question

Write in​ point-slope form an equation of the line through the pair of points. (3,12) and (5,9)

Answer 1

`\large\boxed{y=-(3)/(2)x+16(1)/(2)\to y=-1.5x+16.5}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (3, 12) and (5, 9).

Substitute:

`m=(9-12)/(5-3)=(-3)/(2)=-(3)/(2)`

Put the value of a slope and coordinates of the point (3, 12) to the equation of a line:

`12=-(3)/(2)(3)+b`

`12=-(9)/(2)+b`

`12=-4(1)/(2)+b` add
`4(1)/(2)` to both sides

`16(1)/(2)=b\to b=16(1)/(2)`

Finally:

`y=-(3)/(2)x+16(1)/(2)`