Question

QUESTION 1:

Answer 1

Q1

I like to use the standard form to write the equation of a perpendicular line, especially when the original equation is in that form. The perpendicular line will have the x- and y-coefficients swapped and one negated (remember this for Question 3). Thus, it will be

... 5x - 2y = 5(6) - 2(16) = -2

Solving for y (to get slope-intercept form), we find

... y = (5/2)x + 1 . . . . . matches selection C

Q2

The given equation has slope -3/6 = -1/2, so that will be the slope of the parallel line. (matches selection A)

Q3

See Q1 for an explanation. The appropriate choice is ...

... B. 4x - 3y = 5

Q4

The given line has slope -2, so you can eliminate all choices except ...

... D. -2x

Q5

The two lines have the same slope (3), but different intercepts, so they are ...

... A. parallel

Answer 2

Answer:

1). Given: Point ( 6 , 16 ) and equation of line is 2x + 5y = 4

First we find the slope of given line by writing it in slope intercept form.

$5y=-2x+4$

$y=\frac{-2}{5}x+\frac{4}{5}$

So, the slope is -2/5

We also knows that product of slopes of perpendicular lines equal to -1

let slope of required line is m the,

$m\times\frac{-2}{5}=-1$

$m=\frac{5}{2}$

Now, The equation of required line ,

$y-16=\frac{5}{2}(x-6)$

$y=\frac{5}{2}x-\frac{5}{2}\times6+16$

$y=\frac{5}{2}x-15+16$

$y=\frac{5}{2}x+1$

Therefore, Option C is correct.

2). Given: equation of line is 3x + 6y = 9

we find the slope of given line by writing it in slope intercept form.

$6y=-3x+9$

$y=\frac{-3}{6}x+\frac{9}{6}$

So, the slope is -3/6 = -1/2

We also knows that Slope of parallel lines are same.

Therefore, Option A is correct.

3). Given: equation of line is 3x + 4y = 7

First we find the slope of given line by writing it in slope intercept form.

$4y=-3x+7$

$y=\frac{-3}{4}x+\frac{7}{4}$

So, the slope is -3/4

We also knows that product of slopes of perpendicular lines equal to -1

let slope of required line is m the,

$m\times\frac{-3}{4}=-1$

$m=\frac{4}{3}$

Now, we check slope of each option.

Option A- 4x + 3y = 3

                y = -4/3x + 3/3

⇒ Slope = -4/3

Option B- 4x - 3y = 3

                y = 4/3x - 3/3

⇒ Slope = 4/3

 Therefore, Option B is correct.

4). Given: Point ( -2 , 4 ) and equation of line is 2x + y = 4

First we find the slope of given line by writing it in slope intercept form.

$y=-2x+4$

So, the slope is -2

We also knows that Slope of parallel lines are equal.

Thus, slope of required line is -2

Now, The equation of required line ,

$y-4=-2(x-(-2))$

$y=-2x-4+4$

$y=-2x$

Therefore, Option D is correct.

5). Given: equations of line are 3x - y = -7 and 6x - 2y = 1

First we find the slope of given lines by writing it in slope intercept form.

3x - y = -7

y = 3x + 7

So, Slope of 1st line = 3

$6x-2y=1$

$y=\frac{6}{2}x-\frac{1}{2}$

So, the slope of 2nd line is 6/2 = 3

Since slope of both lines are equal. given lines are parallel.

Therefore, Option A is correct.