Q. 8

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

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Answer

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

1Step 1. Given information.

We have two equation.

$y = 2 x + 3$

$y = a x + 5$

2Step 2. Fill the blank.

As we know that parallel lines are two straight lines that never touch. Therefore, parallel lines have the same slope, but different $y -$ intercept.

Compare the given two equation with slope-intercept form $y = m x + b$ , we get:

$m_{1} = 2 m_{2} = a$

Since two lines are parallel, it follows:

$m_{1} = m_{2} 2 = a a = 2$

Therefore, the value of $a$ is $2$ .