Chapter 1.3, Problem 8AYU

To determine

To fill in: the given blank

Answer to Problem 8AYU

The lines $y=2x+3$ and $y=ax+5$ are parallel if $a=2$ .

Explanation of Solution

Given:

The lines $y=2x+3$ and $y=ax+5$ are parallel if $a=\_\_\_\_\_\_$ .

Calculation:

The two lines are said to be parallel only when they have the same slope. Since the given lines are in the slope-intercept form, the slope of the first line is 2.

The line $y=ax+5$ becomes parallel to $y=2x+3$ only when $a=2$ .

Thus, the given statement can be completed as “The lines $y=2x+3$ and $y=ax+5$ are parallel if $a=2$ .”

Conclusion:

Therefore, the lines $y=2x+3$ and $y=ax+5$ are parallel if $a=2$ .”