Chapter SH, Problem 4.9EP

To determine

To determine whether the graph of lines $y=-2x+6$ and $2y=x-3$ are parallel or perpendicular.

Answer to Problem 4.9EP

The lines $y=-2x+6$ and $2y=x-3$ are perpendicular.

Explanation of Solution

Given information:

The lines are $y=-2x+6$ and $2y=x-3$

Calculation:

Slope intercept form: The graph of the equation $y=mx+b$ (where m and b are real numbers) is a line with slope, m, and y-intercept, b.This form of the equation of a line is called the slope-intercept form.

Let L1: $y=-2x+6$

Let L2: $2y=x-3$

Rewrite equation L2 into slope intercept form

  $L2:y=\frac{1}{2}x-\frac{3}{2}$

Using slope intercept form to find slope of L1 Slope of L1: $m_1=-2$

Using slope intercept form to find slope of L2

Slope of L2: $m_2=\frac{1}{2}$

Product of slopes

  $m_1\times m_2=-2\times \frac{1}{2}$

On solving,

  $m_1\times m_2=-1$

When the product of the slope of two lines is -1.

Then, lines will be perpendicular.

Here, the product of slope of L1 and L2 is -1.

Hence, the lines are perpendicular.