Question

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Answer 1

As a first step, choose two sets of coordinates for two lines.

Answer 2

Find the equation of the line passing through: (13, 23), (12, 17)

Answer 3

Find the slope. m = (y2-y1)/(x2-x1)

Answer 4

Yes. y = mx + b
y = 6x + b
It passes through (13,23)
(you can choose the second point also and you will get the same answer)
put x = 13, y = 23 in y = 6x + b
23 = 6(13) + b
find b

Answer 5

We wanted to find the equation of a line passing through (13, 23) and (12, 17)
The general equation of a line in slope-intercept form is: y = mx + b
where m is the slope and b is the y-intercept (on a graph that is where the line will cross the y-axis).
We found the slope m = 6 and so the line equation is y = 6x + b
We still need to find b.
Since the line passes through the point (13,23) the point must satisfy the line equation.
Put x = 13 and y = 23 into the line equation and solve for b.
23 = 6(13) + b
23 = 78 + b
b = 23 - 78 = -55
The equation of the line is: y = 6x - 55

Answer 6

If you take the equation y = 6x - 55 you can verify that it contains BOTH points (13, 23) and (12, 17). Let us make sure.
y = 6x - 55
put x = 13 and y = 23
23 = 6(13) - 55 = 78 - 55 = 23
so it satisfies. Try the other point too,
put x = 12 and y = 17:
17 = 6(12) - 55 = 72 - 55 = 17
second point satisfies the equation as well.

Now use the same procedure to find the equation of the line passing through the second pair of points.

Answer 7

No problem.

Answer 8

Yes, that is the slope.
The general equation is: y = mx + b
put m = 7/2
y = 7/2x + b
This line passes through (16,16)
set x = 16 and y = 16 and solve for b.

Answer 9

It is a fraction. Don't worry about it. It is just another form of a number.

Answer 10

Yes m is the slope and b is the y-intercept,

Answer 11

The line passes through (16,16).
That means x = 16 and y = 16 MUST satisfy the equation.

Set y to 16 also.

Answer 12

No. y = 7/2x + b
x = 16, y = 16
16 = 7/2(16) + b
solve for b

Answer 13

2 in the denominator will go 8 times in 16 in the numerator. Multiply 8 and 7.

Answer 14

\[\frac{ 7 }{ 2 } \times 16 = 7 \times 8 = 56\]

Answer 15

so 16 = 56 + b
b = ?

Answer 16

We have already found the slope. m = 7/2
we need to find b.

Answer 17

The equation you wrote earlier is not correct. I corrected it earlier in one of my replies.

Answer 18

y = 7/2x + b
This line passes through (16,16)
put x = 16 and y = 16
16 = 7/2(16) + b
16 = 56 + b
16-56 = b
b = -40
y = 7/2x - 40

Answer 19

The equation of the first line is: y = 6x - 55
The equation of the second line is: y = 7/2x - 40

The slope of the first line is: 6
The slope of the second line is: 7/2

Since the slopes are not the same, the lines are NOT parallel.

Answer 20

We just finished the second pair of coordinates and found the equation of the line to be: y = 7/2x - 40

Answer 21

Isn't that what we just finished?

Answer 22

Yeah. Those are the four coordinates.
We found the equation of the line that has the two points (13,23) and (12,17).
The equation was y = 6x - 55

Then we found the equation of the line that has the two points (16,16) and ( 18,23).
The equation was y = 7/2x - 40

Answer 23

This problem is not completed yet.

Answer 24

"Show the lines are either parallel or not parallel by showing your work with the slope formula for each line"

The slope of the first line is 6.
The slope of the second line is 7/2

Since the slopes are not the same the lines are NOT parallel.

Answer 25

We still have to do:
"write an equation of a line parallel to one of the lines in slope-intercept form that contains the point (1,-3)."

Answer 26

.Let us pick the first line whose slope is 6.

A line parallel to the first line will also have the same slope.

y = mx + b
y = 6x + b
It passes through the point (1,-3)
put x = 1, y = -3
-3 = 6(1) + b
-3 = 6 + b
b = -3 - 6 = -9

The equation of the line is: y = 6x - 9

Answer 27

I have to leave in about 10 minutes.

Answer 28

BTW, for the first part of the problem, I just realized they just want the slope of the two lines and not the equation of the lines. So you can stop after find the slope of each line for this problem. (Although what we did is a good practice to find the equation of the line).

Answer 29

1: (13, 23), (12, 17)
2: (16, 16), (18, 23)

So for the first part you can say:

slope of the line passing through (13, 23), (12, 17) is: (23-17)/(13-12) = 6
slope of the line passing through (16, 16), (18, 23) is: (23-16)/(18-16) = 7/2

The slopes of the two lines are not the same. Therefore, the lines are not parallel.

Answer 30

Post your next question in a separate post. If I am not there hopefully someone else will answer it.