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Rufina [12.5K]
3 years ago
7

Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept fo

rm)
Mathematics
1 answer:
Alla [95]3 years ago
8 0

Answer:

\displaystyle y=-\frac{1}{2}x+4

Step-by-step explanation:

<u>Equation of a Line</u>

We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.

We are given a line

y - 12 = 2x -8

And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y

y = 2x +4

The coefficient of the x is the slope

m=2

The slope of the perpendicular line is the negative reciprocal of m, thus

\displaystyle m'=-\frac{1}{2}

We know the second line passes through (2,3). That is enough information to find the second equation:

y-y_o=m'(x-x_o)

\displaystyle y-3=-\frac{1}{2}(x-2)

Operating

\displaystyle y=-\frac{1}{2}(x-2)+3

Simplifying

\displaystyle y=-\frac{1}{2}x+4

That is the equation in slope-intercept form. Intercept: y=4

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