Question

If you multiply the slopes of two perpendicular lines, the product is −1. (As long as neither line is vertical.) Use that fact and the graph to complete the statements below.

Answer 1

Explanation:

Answer 2

Part 1) The number in the blank box is
`2`

Part 2) The slope of the line h is
`m=2`

Part 3) The equation of the line h is
`y=2x+4`

Explanation:

Statement A

we know that

If two lines are perpendicular, the product of their slopes is equal to -1

so

m1*m2=-1

In this problem we have

`m1=-(1)/(2)`

substitute in the formula and solve for m2

`-(1)/(2)*m2=-1`

Multiply by -2 both sides

`m2=2`

Statement B

we know that

The line h is perpendicular to the line g

therefore

The slope of the line h is equal to
`m=2`

Statement C

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 y-coordinate of the y-intercept

Find the equation of the line h

we have

`m=2`

`b=4` -----> observing the graph

substitute the values

`y=2x+4`