Mathematics, 10.01.2021 14:00 skyemichellec

What is an equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5?

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Answer from: zakeiryh

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is $y=-\frac{1}{2}x-1$

Given:

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5

First we find the slope of given equation 2x-y=5

y=mx+b is the equation of the line . where 'm' is the slope

$2x-y=5\\2x-5=y\\y=2x-5$

Slope m=2.

Slope of perpendicular lines are negative reciprocal of one another

Slope of perpendicular line is $-\frac{1}{2}$

The line passes through the point (6,-4)

Use the point and slope to get the equation of the perpendicular line

slope m = $-\frac{1}{2}$

Point slope form of line is

$y-y_1=m(x-x_1)\\y+4=-\frac{1}{2}(x-6)\\y+4=-\frac{1}{2}x+3\\y=-\frac{1}{2}x-1$

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is $y=-\frac{1}{2}x-1$

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Answer from: wowihavefun

An equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:

$y=-\frac{1}{2}x-1$

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the line

2x-y=5

converting the line into slope-intercept form

y = 2x-5

comparing with the slope-intercept form of the line equation

The slope of the line = m = 2

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 2

Thus, the equation of new line = – 1/m = -1/2 = -1/2

using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of the slope = -1/2 and the point (6,−4)

$y-\left(-4\right)=-\frac{1}{2}\left(x-6\right)$

$y+4=-\frac{1}{2}\left(x-6\right)$

Subtract 4 from both sides

$y+4-4=-\frac{1}{2}\left(x-6\right)-4$

$y=-\frac{1}{2}x-1$

Therefore, an equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:

$y=-\frac{1}{2}x-1$

Answer from: Quest

maybe i can

Answer from: Quest

For a 0.25 pfor b o.3pp (0.25+0.3)=0.28

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