Question

The equation of line LM is 5x − y = −4. What is the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2)?
a) y = 5x + 13
b) y = negative one fifthx + seven fifths
c) y = negative one fifthx − seven fifths
d) y = 5x − 17

Answer 1

Answer: b) y = negative one fifthx + seven fifths

Step-by-step explanation:

Equation of a line in Slope intercept form : $y=mx+c$   (1)

, where m is slope and c is constant.

Given : The equation of line LM is $5x - y = -4.$

Convert it into slope- intercept form, we get

$y=5x+4$

Comparing it to (1) , we get

$m= 5$

Let $m_1$ be the slope pf the line perpendicular to LM.

Since the product of slopes of two perpendicular lines is -1.

Therefore , $m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}$

Equation of line passing through (-3,2) and having slope $m_1=\dfrac{-1}{5}$ will be :-

$(y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}$

Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is $y=\dfrac{-1}{5}x+\dfrac{7}{5}$.

Hence, the correct answer is b) y = negative one fifthx + seven fifths.

Answer 2

We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5

Perpendicular lines.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:

y = (-1/a)*x + c

Now we start with the line that we know, we need to find its slope:

5x - y = -4

We need to isolate y

y = 5x + 4

Then the slope of this line is a = 5, so the perpendicular line will be:

y = (-1/5)*x + c

Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:

2 = (-1/5)*-3 + c

2 = (3/5) + c

2 - 3/5 = c

10/5 - 3/5 = c

7/5 = c

Then the equation is:

y = (-1/5)*x + 7/5

So the correct option is b.

If you want to learn more about linear equations, you can read:

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