Question 1: which is the equation in slope-intercept form for the line that passes through (6, 16) and is perpendicular to 2x + 5y = 4? a. y = - 2/5 x + 18 b. y = 2/5 x + 14 c. y = 5/2 x + 1 d. y = - 5/2 x + 31 question 2: what is the slope of a line parallel to the line whose equation is 3x + 6y = 9? a. -1/2 b. 1/2 c. 2 d. 3 question 3: which is the equation of a line perpendicular to the line with the equation 3x + 4y = 7? a. 4x + 3y = 3 b. 4x - 3y = 5 c. 3x - 4y = 3 d. 3x + 4y =5 question 4: which is the equation in slope-intercept form for the line that passes through (-2, 4) and is parallel to 2x + y = 4? a. y = 1/2x + 5 b. y = -1/2x + 3 c. y = 2x + 8 d. y = -2x question 5: which best describes the relationship between the lines? 3x - y = -7 6x - 2y = 1 a. parallel b. perpendicular c. neither d. same line

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.

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,

Now, The equation of required line ,

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.

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.

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,

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.

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 ,

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

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.

a

step-by-step explanation: