Question

PLEASE HELP

Answer 1

Answer:

$\displaystyle y=-\frac{1}{2}x+\frac{11}{2}$

Step-by-step explanation:

Equation of the Line

A line of slope m and y-intercept b can be expressed by the equation:

$y=mx+b$

The given line has the equation:

$8x-4y=-24$

Let's express it in the correct form:

$-4y=-24-8x$

Dividing by -4

$y=2x+6$

The slope of this line is m1=2. To find the slope m2 of a line perpendicular to this one, we use the following equation:

$m_1.m_2=-1$

Solving for m2:

$\displaystyle m_2=-\frac{1}{m_1}$

$\displaystyle m_2=-\frac{1}{2}$

The required equation has the form:

$\displaystyle y=-\frac{1}{2}x+b$

To find b, we use the point (3,4) through which the line passes:

$\displaystyle 4=-\frac{1}{2}(3)+b$

$\displaystyle b=4+\frac{3}{2}=\frac{11}{2}$

Thus the equation of the line is:

$\boxed{\displaystyle y=-\frac{1}{2}x+\frac{11}{2}}$