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9966 [12]
3 years ago
11

Perpendicular to the line y=1/2x-8; passes through (7,-6). Write the slope-intercept form of the equation.

Mathematics
1 answer:
Airida [17]3 years ago
6 0

<u>ANSWER: </u>

The slope intercept form of the required line is y = -2x + 20.

<u>SOLUTION: </u>

Given, line equation is $y=\frac{1}{2} x-8$

And, Perpendicular line to the given line  passes through (7,-6).  

We need to find the slope intercept form of perpendicular line of given line.  

We already have the point (7, -6) but we need to find the slope.

Now, we know that, product of slopes of two perpendicular lines equals to -1.

Slope of given line is \frac{1}{2}, by comparing with the general form of slope intercept form.

\frac{1}{2} \times slope of required line = -1

Slope of perpendicular line = -2

Now, line equation of perpendicular line in point slope form is

$y-y_{1}=m\left(x-x_{1}\right)$

y – (-6) = -2(x – 7)

y + 6 = -2x + 14

y = -2x + 20

the above equation is in the form of slope intercept form of a line equation  

where slope m = -2 and intercept c = 20

hence, the slope intercept form of the required line is y = -2x + 20.

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