Write Equation of a line that goes through (8,5) and is perpendicular to 2x-y=7 in slope intercept form and standard form

rancuri5a
2022-09-30
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tiepidolu

Answered 2022-10-01
Author has **8** answers

Converting 2x−y=7 into a slope-intercept form:

y=2x+7

The slope of 2x−y=7 is 2

So the slope of the requiblack line is $-\frac{1}{2}$

(the slopes of perpendicular lines are the negative inverse of each other)

We are looking for a line with slope $m=-\frac{1}{2}$ which passes through

$({x}_{1},{y}_{1})=(8,5)$

In slope-point form this is

$(y-5)=(-\frac{1}{2})(x-8)$

Converting to slope intercept form:

$y=-\frac{1}{2}x+9$

and in standard form

$x+2y=18$

y=2x+7

The slope of 2x−y=7 is 2

So the slope of the requiblack line is $-\frac{1}{2}$

(the slopes of perpendicular lines are the negative inverse of each other)

We are looking for a line with slope $m=-\frac{1}{2}$ which passes through

$({x}_{1},{y}_{1})=(8,5)$

In slope-point form this is

$(y-5)=(-\frac{1}{2})(x-8)$

Converting to slope intercept form:

$y=-\frac{1}{2}x+9$

and in standard form

$x+2y=18$

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I am having difficulty with true/false statements and their justifications regarding systems of linear equations.

(a) A linear system of three equations in five unknowns is always consistent (i.e. it has at least one solution)

(b) A linear system of five equations in three unknowns cannot be consistent

(c) If a linear system in echelon form is triangular then the system has the unique solution

(d) If a linear system of n equations in n unknowns has two equations that are multiples of one another, then the system is inconsistent.

So far, for (a) I have said False, as it will always be consistent if it is homogeneous, but not if it is non-homogeneous.

For (b) I have said false, but am having difficulty justifying this assertion

c) I know to be true.

(d) I believe may be false as having equations that are multiples could result in free variables and hence infinite solutions?

I am rather unsure on what I have done so far.

Any assistance is greatly appreciated.

(a) A linear system of three equations in five unknowns is always consistent (i.e. it has at least one solution)

(b) A linear system of five equations in three unknowns cannot be consistent

(c) If a linear system in echelon form is triangular then the system has the unique solution

(d) If a linear system of n equations in n unknowns has two equations that are multiples of one another, then the system is inconsistent.

So far, for (a) I have said False, as it will always be consistent if it is homogeneous, but not if it is non-homogeneous.

For (b) I have said false, but am having difficulty justifying this assertion

c) I know to be true.

(d) I believe may be false as having equations that are multiples could result in free variables and hence infinite solutions?

I am rather unsure on what I have done so far.

Any assistance is greatly appreciated.

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