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

Answer:

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

Step-by-step 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. $m_1=-\frac{1}{m_2}$

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)

$y=mx+b\\2=\frac{1}{4}(4)+b\\2=b$

So, we get b = 2

Now, Equation of line

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

$y=mx+b\\y=\frac{1}{4}x+2$

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