Question

I graphed y=3x+1 on a number graph and now I need to write an equation for the line parallel to the line on that graph that passes through (2,0) can anyone help me do this step by step?

Answer 1

y = 3x + 1
What is the slope of this line?

Answer 2

(1,0)

Answer 3

if thats correct

Answer 4

That is not the slope.
The general equation of a line in the slope-intercept form is y = mx + b.
'm' is the slope and 'b' is the y-intercept.

Answer 5

i wan't told to solve the problem just to graph it, so I typed the equation into mathway and I was given the points to plot it on

Answer 6

so no slope

Answer 7

But this question asks for the equation of a line parallel to the line y = 3x + 1 and passing through the point (2,0). To find the equation we now need to first find the slope of the line y = 3x + 1.

Answer 8

i'm going to send a picture to help if i may

Answer 9

That is part A. The graph has to be steeper than that. Doesn't look right.

Answer 10

part B is right below it! that's what this question was about, and I believe that is right due to google and mathway telling me thats the way it should look but it could be wrong

Answer 11

y = 3x + 1 represents a straight line.
To draw a straight line all you need are ANY two points on the line.
You don't need mathway or Google to do that.
Just find two points on the line.

y = 3x + 1
put x = 0: y = 3*0 + 1 = 1
(0, 1) is one point.
put x = 1: y = 3*1 + 1 = 4
(1, 4) is another point.
Plot those two points on the graph paper.
Then using a ruler draw a line passing through those two points.

Answer 12

alright i just need to plot the points one minute

Answer 13

I will come back after for you post the pic of the corrected graph.

Answer 14

excuse the bad handwriting

Answer 15

@aum

Answer 16

Correct.

Answer 17

For part B) they want an equation of a line parallel to y = 3x + 1 and passing through the point (2,0).

Parallel lines have the SAME slope.
What is the slope of the line y = 3x + 1.
Compare this equation to the general form y = mx + b where 'm' is the slope.
we can see 3 is the slope of the line y = 3x + 1.

Therefore, the slope of the line we want is 3 so that it will be parallel.
Put m = 3 in y = mx + b
y = 3x + b
This line has to pass through (2,0)
That is, when x = 2, y = 0
0 = 3*2 + b
0 = 6 + b
b = -6

y = 3x - 6 is the equation of the line parallel to the line y = 3x + 1 and passes through the point (2,0).

Answer 18

i apologize if i dont respond right away the website is acting up but keep going please!

Answer 19

may i show you part c quick in case i keep crashing, unless you dont have time.

Answer 20

It is done. They just want the equation and it is solved above. They don't want graph for this one.

Answer 21

go ahead.

Answer 22

C) Two lines are perpendicular if the product of their slopes is -1.
Slope of the line y = 3x + 1 is 3.
Let y = mx + b be the slope of the perpendicular line. The slope of this line is m.
Since the two lines are perpendicular, the product of their slopes, 3 * m = -1
Therefore, m = -1/3
The perpendicular line is: y = -1/3x + b
It passes through (0, -4)
when x = 0, y = -4
-4 = -1/3 * 0 + b
b = -4
y = -1/3x - 4
is the equation of the perpendicular line.

Answer 23

this is starting to make sense now! do you think you have time for the bonus question as well?

Answer 24

I will do one more.

Answer 25

wait I think you made a mistake in the last question

Answer 26

at the last part did you mean to put
when x = 0, y = -4 -4 = -1/3 * 0 + b b = -4 y = -1/3x - 4 is the equation of the perpendicular line.

Answer 27

there are two -4 and bs in a row

Answer 28

it's confusing me a bit :(

Answer 29

@aum no rush just making sure you know i'm still here

Answer 30

wait i got it!

Answer 31

heres the bonus question

Answer 32

oh god thats small

Answer 33

can't see.

Answer 34

it says: the standard form of a linear equation is Ax+By=C. On another page, transform this into the slope-intercept form using A,B,C,x, and y

Answer 35

Ax + By = C (Standard form of a linear equation).
To put it in slope-intercept form, we need to put it in the form y = mx + b.
Ax + By = C
Solve for y. Isolate y:
Add -Ax to both sides:
By = -Ax + C
divide by B:
\[y = -\frac ABx + \frac CB \] is the slope-intercept form.

Answer 36

awesome : D thank you so much for your help i made you best response and fanned you dont worry

Answer 37

you are welcome.