Question

identifying slope and y-intercept of a line
identify the slope and y-intercept of each linear function’s equation.
$y = 1 - 3x$
$-x + 3 = y$
$y = 3x - 1$
$x - 3 = y$
slope = -1; y-intercept at 3
slope = 3; y-intercept at -1
slope = 1; y-intercept at -3
slope = -3; y-intercept at 1

Explanation:

For \( y = 1 - 3x \)

Step 1: Rewrite in slope - intercept form (\( y=mx + b \))

The slope - intercept form of a linear equation is \( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \) - intercept. Rewrite \( y = 1-3x \) as \( y=-3x + 1 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y = mx + b \), we have \( m=-3 \) (slope) and \( b = 1 \) (\( y \) - intercept). So it matches with "slope \(=-3 \); \( y \) - intercept at 1".

For \( -x + 3=y \)

Step 1: Rewrite in slope - intercept form

Rewrite \( -x + 3=y \) as \( y=-x + 3 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y=mx + b \), \( m=-1 \) (slope) and \( b = 3 \) (\( y \) - intercept). So it matches with "slope \(=-1 \); \( y \) - intercept at 3".

For \( y = 3x-1 \)

Step 1: Compare with slope - intercept form

The equation \( y = 3x-1 \) is in the form \( y=mx + b \).

Step 2: Identify slope and \( y \) - intercept

Here, \( m = 3 \) (slope) and \( b=-1 \) (\( y \) - intercept). So it matches with "slope \( = 3 \); \( y \) - intercept at \( -1 \)".

For \( x - 3=y \)

Step 1: Rewrite in slope - intercept form

Rewrite \( x - 3=y \) as \( y=x-3 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y=mx + b \), \( m = 1 \) (slope) and \( b=-3 \) (\( y \) - intercept). So it matches with "slope \( = 1 \); \( y \) - intercept at \( -3 \)".

Final Matching:

• \( y = 1-3x \) \(

ightarrow\) slope \(=-3 \); \( y \) - intercept at 1

• \( -x + 3=y \) \(

ightarrow\) slope \(=-1 \); \( y \) - intercept at 3

• \( y = 3x-1 \) \(

ightarrow\) slope \( = 3 \); \( y \) - intercept at \( -1 \)

• \( x - 3=y \) \(

ightarrow\) slope \( = 1 \); \( y \) - intercept at \( -3 \)

Answer:

For \( y = 1 - 3x \)

Step 1: Rewrite in slope - intercept form (\( y=mx + b \))

The slope - intercept form of a linear equation is \( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \) - intercept. Rewrite \( y = 1-3x \) as \( y=-3x + 1 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y = mx + b \), we have \( m=-3 \) (slope) and \( b = 1 \) (\( y \) - intercept). So it matches with "slope \(=-3 \); \( y \) - intercept at 1".

For \( -x + 3=y \)

Step 1: Rewrite in slope - intercept form

Rewrite \( -x + 3=y \) as \( y=-x + 3 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y=mx + b \), \( m=-1 \) (slope) and \( b = 3 \) (\( y \) - intercept). So it matches with "slope \(=-1 \); \( y \) - intercept at 3".

For \( y = 3x-1 \)

Step 1: Compare with slope - intercept form

The equation \( y = 3x-1 \) is in the form \( y=mx + b \).

Step 2: Identify slope and \( y \) - intercept

Here, \( m = 3 \) (slope) and \( b=-1 \) (\( y \) - intercept). So it matches with "slope \( = 3 \); \( y \) - intercept at \( -1 \)".

For \( x - 3=y \)

Step 1: Rewrite in slope - intercept form

Rewrite \( x - 3=y \) as \( y=x-3 \).

Step 2: Identify slope and \( y \) - intercept

Comparing with \( y=mx + b \), \( m = 1 \) (slope) and \( b=-3 \) (\( y \) - intercept). So it matches with "slope \( = 1 \); \( y \) - intercept at \( -3 \)".

Final Matching:

• \( y = 1-3x \) \(

ightarrow\) slope \(=-3 \); \( y \) - intercept at 1

• \( -x + 3=y \) \(

ightarrow\) slope \(=-1 \); \( y \) - intercept at 3

• \( y = 3x-1 \) \(

ightarrow\) slope \( = 3 \); \( y \) - intercept at \( -1 \)

• \( x - 3=y \) \(

ightarrow\) slope \( = 1 \); \( y \) - intercept at \( -3 \)