Question

What is the slope of a line that is perpendicular to the graphed line?

Answer 1

The slope of the line perpendicular to the graphed line is 2.

Explanation:

The Slope of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

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

The graphed line passes through two visible points (0,4) and (8,0). Thus, its slope is:

`\displaystyle m=(0-4)/(8-0)`

`\displaystyle m=(-4)/(8)`

Simplifying:

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

Two lines of slopes m1 and m2 are perpendicular is:

`m_1.m_2=-1`

Suposse the given line has slope
`m_1=-(1)/(2)`. To find m2, we solve the above equation:

`\displaystyle m_2=-(1)/(m_1)`

Substituting:

`\displaystyle m_2=-(1)/(-(1)/(2))`

Operating

`m_2=2`

The slope of the line perpendicular to the graphed line is 2.