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kati45 [8]
3 years ago
7

PLEASE HELP

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0

Answer:

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

Step-by-step explanation:

<u>Equation of the Line</u>

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}}

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