Question

1. These four lines have been graphed on the same coordinate grid. Which lines are parallel to each other?
line j: y=1/4x+4
line k: y=1/4x+3
line l: y=3x+4
line m: y=4x+1/4

a. j and k
b. j and m
c. l and k
d. l and m

2. Find the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2).
a. y=-3x+2
b. y=-3x+3
c. y=-1/3x+2
d. y=-1/3x+3

3. Find the point, M, that divide segment segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).
a. (6, 12)
b. (-6, 12)
c. (6, -12)
d. (-6, -12)

4. Find the distance between (4, 2) and (-4, -4).
a. 2
b. square root of 10
c. 4
d. 10

Answer 1

1. lines j and k because they have the same slope.
2.d because -1/3 is the opposite slope of 3 and it passes through that point.

Answer 2

Answer:

1)a. j and k

2) d. $y =  \frac{-1}[3}x+3$

3)a. (6, 12)

4)d. 10

Step-by-step explanation:

1) Lines are said to parallel if their slopes are same.

General form of line = $y = mx+c$  --1

where m is the slope

On comparing all lines with 1

So, Slope of line j = $\frac{1}{4}$

Slope of line k = $\frac{1}{4}$

Slope of line l = 3

Slope of line m = 4

Slope of line j and k are same

So, Option a is correct.

a. j and k

2) Find the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2).

y=-8+3x

On comparing with 1

Slope of given line is 3

Now slope of a line which is perpendicular to the given line

Two lines are said to be perpendicular if the product of their slopes is -1

So, $3 \times \frac{-1}{3}=-1$

So, slope of perpendicular line is  $\frac{-1}{3}$

General form of line = $y = mx+c$  -1

Substitute m = $\frac{-1}{3}$ and passing points (3,2)

$2 = 3\times \frac{-1}[3}+c$

$3=c$

So, Now substitute value of m and c in 1

$y =  \frac{-1}[3}x+3$

Hence the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2) is $y =  \frac{-1}[3}x+3$

Option d is correct.

3) Find the point, M, that divide segment segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

m:n=5:2

$(x_1,y_1)=(1,2)$

$(x_2,y_2)=(8,16)$

To find coordinates of M we will sue section formula:

$x=\frac{mx_2+nx_1}{m+n}$ and $y=\frac{my_2+ny_1}{m+n}$

$x=\frac{5(8)+2(1)}{5+2}$     and $y=\frac{5(16)+2(2)}{5+2}$

$x=\6$     and $y=12$

Thus the coordinates of M is (6,12)

Hence Option A is correct.

4). Find the distance between (4, 2) and (-4, -4).

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(4,2)$

$(x_2,y_2)=(-4,-4)$

Substitute the values in the formula :

$d=\sqrt{(-4-4)^2+(-4-2)^2}$

$d=\sqrt{(-8)^2+(-6)^2}$

$d=\sqrt{64+36}$

$d=\sqrt{100}$

$d=10$

Thus the distance is 10

Hence Option D is correct.