1). write an equation of a line with the given slope and y-intercept.
m= -2, b=4
a) y= -2x-4
b) y= -2x+4
c) y= -1/2x+4
d) y= 4x-2
2). find the slope and y-inercept of the line
y= 1/5x-8
a). 5; 8
b). 8; 1/5
c). 1/5; -8
d). -8; 1/5
3). are the graphs of the lines in he pair parallel? explain
y=6x+9
27x-3y=-81
a). yes, since the slopes are the same and the y-intercepts are the same.
b). yes, since the slopes are the same and the y-intercepts are different.
c). no, since the y-intercepts are different.
4). write y=3/5x+4 in a standard form using integers.
a). -3+5y=10
b). 5x-3y=20
c). -3x+5y=4
d). -3x-5y=20
5). write an equation for the line that is parallel to the given line and that passes through the given point.
y=2x+7; (3,11)
a). y= -1/2x-5
b). y= 2x+5
c). y= 1/2x+5
d). y= 2x-19

can someone me with this ? i seem to be struggling a lot with i'll mark a brainliest if you want after you will be much appreciated

Answers:

1) The Equation of a Line is:

   (1)

Where:

is the slope

is the y-intercept

For this problem we have a given and a given

So, we only have to substitute this values in the equation (1):

This is option B

2) Here we have to find the slope and the y-intercept of this equation:

According to the explanation in the first answer related to the equation (1), the slope of this line is:

And its y-intercept is:

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

   (a)

   (b)

Equation (b) has to be written in the same form of (a), in the form in order to be able to compare both:

   (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write in a standard form with integers:

Multiply each side by 5:

In this case none of the options apply, please check if the question was written correctly.

5) In this question we are asked to write an equation parallel to:

    (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:

Equation of the slope:

   (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

Finally:

This is option B

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: