AnswersMO-Algebra I ARecognizing Patterns

Point-Slope Form of a Line Answers

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Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use:Step 1: Choose a point on the line, such as (2, 5).Step 2: Choose another point on the line, such as (1, 3).Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is .Step 4: Substitute those values into the point-slope form.y – y1 = m(x – x1)y – 3 = (x – 1)Which of Talia’s steps is incorrect?

Question illustration
A
Step 1 is incorrect because it uses a point that is not on the line.
B
Step 2 is incorrect because it uses a point that is not on the line.
C
Step 3 is incorrect because it shows an incorrect ratio for the slope.
D
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ?

Question illustration
A
y + 2 =(x + 3)
Option A
B
y – 2 = (x – 3)
Option B
C
y + 3 = (x + 2)
Option C
D
y – 3 = (x – 2)
Option D
3

Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?

A
y – 7 = 3(x – 1)
B
y – 1 = 3(x – 7)
C
y – 7 = 4(x – 1)
D
y – 1 = 4(x – 7)
4

Which equation represents a line that passes through (5, 1) and has a slope of ?

Question illustration
A
y – 5 = (x –1)
Option A
B
y – = 5(x –1)
Option B
C
y – 1 = (x –5)
Option C
D
y – 1 = 5
Option D
5

Anya graphed the line (y−2)=3(x−1) on the coordinate grid.

Question illustration
A
−3
B
−1
C
1
D
3
6

Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?

A
f(x) = –3x – 6
B
f(x) = –3x – 4
C
f(x) = –3x + 16
D
f(x) = –3x + 14
7

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

A
y – 9 = –6(x – 3)
B
y + 9 = –6(x + 3)
C
y – 3 = –6(x – 9)
D
y + 3 = –6(x + 9)
8

Which graph matches the equation y+3=2(x+3)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Which equation represents a line that passes through (4, ) and has a slope of ?

Question illustration
A
y – = (x – 4)
Option A
B
y – = (x – 4)
Option B
C
y – = 4(x – )
Option C
D
y – 4 = (x – )
Option D
10

What is the slope of the line with equation y−3=(x−2)?

Question illustration
A
–2
B
Option B
C
StartFraction one-half EndFraction
Option C
D
2

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