Question

Write the slope-intercept form of the equation that passes through the given points. (separate equations for each of them)

1. (10,-3) (5,-2)
2. (6,2) (7,5)
3. (4,4) (-7,4)

Answer 1

Part 1)
`y=-(1)/(5)x-1`

Part 2)
`y=3x-16`

Part 3)
`y=4`

Explanation:

we know that

The equation of the line into slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

Part 1) we have

(10,-3) (5,-2)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(-2+3)/(5-10)`

`m=(1)/(-5)`

`m=-(1)/(5)`

Find the value of b

we have

`m=-(1)/(5)`

`point (10,-3)`

substitute in the equation
`y=mx+b` and solve for b

`-3=-(1)/(5)(10)+b`

`-3=-2+b`

`b=-3+2=-1`

substitute

`y=-(1)/(5)x-1`

Part 2) we have

(6,2) (7,5)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(5-2)/(7-6)`

`m=(3)/(1)`

`m=3`

Find the value of b

we have

`m=3`

`point (6,2)`

substitute in the equation
`y=mx+b` and solve for b

`2=3(6)+b`

`2=18+b`

`b=2-18=-16`

substitute

`y=3x-16`

Part 3) we have

(4,4) (-7,4)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(4-4)/(-7-4)`

`m=(0)/(-11)`

`m=0`

This is a horizontal line (parallel to the x-axis)

The y-intercept b is equal to the y-coordinate

therefore

The equation of the line is

`y=4`