Question

REVIEW: Find the slope for the following situations. a. Given the equation y = 5x + 1 b. Given the equation 2x + y = 6 c. Given the points: (2, 3) and (5, 9)

Answer 1

Part 1) The slope is
`m=5`

Part 2) The slope is
`m=-2`

Part 3) The slope is
`m=2`

Explanation:

Part 1) 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-coordinate of the y-intercept

In this problem we have

`y=5x+1`

so

the slope is
`m=5`

Part 2) we know that

The equation of the line in standard form is equal to

`Ax+By=C`

where

the slope is equal to
`m=-(A)/(B)`

in this problem we have

`2x+y=6`

so

`A=2,B=1,C=6`

substitute

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

`m=-2`

Part 3) we know that

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

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

we have

`A(2,3)\ B(5,9)`

Substitute the values

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

`m=(6)/(3)`

`m=2`