AnswersKY-Math 8 A 1st nine weeks Plus Edgneuity HB - 421Writing Linear Equations Given Two Points

Writing Linear Equations Given Two Points Answers

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The first step of writing an equation when given two points is the same for both strategies, slope-intercept or point-slope forms. What would be the first step in finding the equation of the line that passes through (5, 1) and (3, 5)?

A
create a graph using the two points
B
find the slope
C
find the y-intercept
D
substitute one point’s coordinates into either form
2
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b =

Answer not available
3

y = (1/2)x – 8✔ y = -2x + 2y = 2x – 14y = -2x – 8

Answer not available
4

The equation of line B is .

Answer not available
5

m =

Answers:
Selection 1:-2
Selection 2:2
Selection 3:y = -2x + 2
6

y = one-third x + 3

Question illustration
A
y = –3x + 5
B
y = 3x – 5
C
y = one-third x + 3
Option C
D
y = negative one-third x + 5
Option D
7

y = x + 67 = –1(–1) + by – 4 = –1 (x – 2)y – 7 = –1 (x – (–1))y – 2 = x – 4y = –x + 6

A
y = x + 6
B
7 = –1(–1) + b
C
y – 4 = –1 (x – 2)
D
y – 7 = –1 (x – (–1))
E
y – 2 = x – 4
F
y = –x + 6
8

In which step did Helena make an error?

A
In step 1, she substituted the x values for y and the y values for x.
B
In step 2, she didn’t use an x and y from the same coordinate pair.
C
In step 3, she solved for the wrong variable.
D
Helena did not make an error.
9

Use point-slope form, y - y1 = m(x - x1), to find the linear equation of a line that passes through the points (2, -1) and (10, 7). y = x +

Answers:
Selection 1:1
Selection 2:-3
10

What can you conclude about the line represented in the table? Select all that apply.

A
Using either slope-intercept or point-slope forms will result in different equations.
B
Using either slope-intercept or point-slope forms will result in the same equation.
C
The slope is .
Option C
D
The slope is .
Option D
E
The y-intercept is 2.
F
The y-intercept is 0.
11

Line A has . The equation of line A is . Line B has . The equation of line B is .

Answers:
Selection 1:no slope
Selection 2:x = -5
Selection 3:a slope of 0
Selection 4:y = -5
12

The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

Answer:

Both Samuel and Helena are correct because both forms can be used to find the equation of a line. In slope-intercept form (y = mx + b), you calculate the slope (m) from the two points and then substitute one point to solve for the y-intercept (b). In point-slope form (y - y1 = m(x - x1)), you calculate the slope and substitute it along with one point directly into the formula, which can then be simplified into slope-intercept form.

13

+

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14

The equation of line A is .

Answer not available
15

Sample Response: Both are correct. Using either form will result in the same equation. The slope-intercept form uses slope and a point to find the y-intercept. Point-slope form uses the slope and a point to solve for y to generate the equation. Which of the following did you include in your response? Select all that apply.Both Samuel and Helena are correct.Both forms result in the same equation.Slope-intercept uses slope and a point to find the y-intercept.Point-slope uses slope and a point to s

A
Both Samuel and Helena are correct.
B
Both forms result in the same equation.
C
Slope-intercept uses slope and a point to find the y-intercept.
D
Point-slope uses slope and a point to solve for y to form the equation.
16

Line B has .

Answer not available

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