Question

12. Reason The graphs of 4x + 12y = 8 and

y = mx + 5 are perpendicular. What is the
value of m?

Answer 1

Answer:
`m=3`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

Then, given the following equation:

`4x + 12y = 8`

You can solve for "y" in order to write this equation in Slope-Intercept form:

`4x + 12y = 8\\\\12y=-4x+8\\\\y=-(1)/(3)x+(2)/(3)`

As you can notice, the slope of this line (which we can call
`m_1`) is:

`m_1=-(1)/(3)`

By definition, the slopes of perpendicular lines are negative reciprocals. Therefore, knowing this, you can determine that the slope fo the graph of
`y = mx + 5` is:

`m=3`