Question

Write the equation of the line passing through the given point that is perpendicular to the

given line.
12. y = - 4x + 7: (4,2)

Answer 1

The equation of the line passing through the given point that is perpendicular to the given line y = - 4x + 7: (4,2) is
`\mathbf{y=(1)/(4)x+2 }`

Explanation:

Write the equation of the line passing through the given point that is perpendicular to the given line.

y = - 4x + 7: (4,2)

The equation of required line will be in slope-intercept form
`y=mx+b` where m is slope and b is y-intercept.

We need to find slope and y-intercept

Finding slope:

When two lines are perpendicular their slopes are opposite reciprocal of each other.
`m_1=-(1)/(m_2)`

So, slope of given line = -4 ( Comparing with
`y=mx+b` m = -4)

Now, slope of required line will be: m =1/4 (Opposite reciprocal)

Finding y-intercept

y-intercept can be found using m = 1/4 and point (4,2)

`y=mx+b\\2=(1)/(4)(4)+b\\2=b`

So, we get b = 2

Now, Equation of line

Equation of line having slope m = 1/4 and y-intercept b = 2 is:

`y=mx+b\\y=(1)/(4)x+2`

So, the equation of the line passing through the given point that is perpendicular to the given line y = - 4x + 7: (4,2) is
`\mathbf{y=(1)/(4)x+2 }`