Find the equation of a line, in slope-intercept fotm of a line that passes through the point (9,2) and is perpendicular to the l

Question

1 year ago

6

ine 2x-y=8

1 answer:

cricket20 [7] · Answer 1 · 2023-07-30T03:48:13+03:00

Considering the definition of perpendicular line, the equation of of perpendicular line is y= - $\frac{1}{2}$ x + $\frac{13}{2}$ .

<h3>Linear equation</h3>

A linear equation o line can be expressed in the form y = mx + b.

where

x and y are coordinates of a point.

m is the slope.

b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

<h3>Perpendicular line</h3>

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

<h3>Equation of perpendicular line in this case</h3>

In this case, the line is 2x-y=8. Expressed in the form y = mx + b, you get:

-y=8 - 2x

y= (-2x +8)÷ (-1)

y= 2x -8

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of 2. So:

2× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (2)

<u><em>slope perpendicular line= -</em></u> $\frac{1}{2}$

So, the perpendicular line has a form of: y= - $\frac{1}{2}$ x + b

The line passes through the point (9, 2). Replacing in the expression for perpendicular line:

2= (- $\frac{1}{2}$ )× 9 + b

2= - $\frac{9}{2}$ + b

2+ $\frac{9}{2}$ = b

Finally, the equation of of perpendicular line is y= - $\frac{1}{2}$ x + $\frac{13}{2}$ .

Learn more about perpendicular line:

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