Question

before identifying the slope m and y-intercept b.
a. $y = -2x$
$m = \underline{\quad}$ $b = \underline{\quad}$
b. $x + y = 8$
$m = \underline{\quad}$ $b = \underline{\quad}$
c. $y = -\frac{1}{2}x - 19$
$m = \underline{\quad}$ $b = \underline{\quad}$
d. $y - 2 = 3x$
$m = \underline{\quad}$ $b = \underline{\quad}$
e. $y = -\frac{1}{5}x + 19$
$m = \underline{\quad}$ $b = \underline{\quad}$
f. $y = \frac{1}{5}x$
$m = \underline{\quad}$ $b = \underline{\quad}$
g. $y + \frac{1}{2}x = 8$
$m = \underline{\quad}$ $b = \underline{\quad}$
h. $y = x$
$m = \underline{\quad}$ $b = \underline{\quad}$
i. $4y - x = -48$
$m = \underline{\quad}$ $b = \underline{\quad}$
j. $x + 2y = -10$
$m = \underline{\quad}$ $b = \underline{\quad}$
k. $y = -x - 3$
$m = \underline{\quad}$ $b = \underline{\quad}$
l. $y = x - 9$
$m = \underline{\quad}$ $b = \underline{\quad}$

Answer:

To solve for the slope \( m \) and \( y \)-intercept \( b \) of each linear equation, we use the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. We rewrite each equation in this form if necessary.

Part A: \( y = -2x \)

The equation is already in slope-intercept form.

• Step 1: Identify \( m \) and \( b \) from \( y = mx + b \).

Here, \( m = -2 \) (coefficient of \( x \)) and \( b = 0 \) (constant term, since there is no additional constant).

Part B: \( x + y = 8 \)

Rewrite in slope-intercept form:

• Step 1: Solve for \( y \): \( y = -x + 8 \).
• Step 2: Identify \( m \) and \( b \).

Here, \( m = -1 \) (coefficient of \( x \)) and \( b = 8 \) (constant term).

Part C: \( y = -\frac{1}{2}x - 19 \)

The equation is already in slope-intercept form.

• Step 1: Identify \( m \) and \( b \).

Here, \( m = -\frac{1}{2} \) (coefficient of \( x \)) and \( b = -19 \) (constant term).

Part D: \( y - 2 = 3x \)

Rewrite in slope-intercept form:

• Step 1: Solve for \( y \): \( y = 3x + 2 \).
• Step 2: Identify \( m \) and \( b \).

Here, \( m = 3 \) (coefficient of \( x \)) and \( b = 2 \) (constant term).

Part E: \( y = -\frac{1}{5}x + 19 \)

The equation is already in slope-intercept form.

• Step 1: Identify \( m \) and \( b \).

Here, \( m = -\frac{1}{5} \) (coefficient of \( x \)) and \( b = 19 \) (constant term).

Part F: \( y = \frac{1}{5}x \)

The equation is already in slope-intercept form.

• Step 1: Identify \( m \) and \( b \).

Here, \( m = \frac{1}{5} \) (coefficient of \( x \)) and \( b = 0 \) (constant term, since there is no additional constant).

Part G: \( y + \frac{1}{2}x = 8 \)

Rewrite in slope-intercept form:

• Step 1: Solve for \( y \): \( y = -\frac{1}{2}x + 8 \).
• Step 2: Identify \( m \) and \( b \).

Here, \( m = -\frac{1}{2} \) (coefficient of \( x \)) and \( b = 8 \) (constant term).

Part H: \( y = x \)

The equation is already in slope-intercept form (can be written as \( y = 1x + 0 \)).

• Step 1: Identify \( m \) and \( b \).

Here, \( m = 1 \) (coefficient of \( x \)) and \( b = 0 \) (constant term).

Part I: \( 4y - x = -48 \)

Rewrite in slope-intercept form:

• Step 1: Solve for \( y \):

\( 4y = x - 48 \)
\( y = \frac{1}{4}x - 12 \).

• Step 2: Identify \( m \) and \( b \).

Here, \( m = \frac{1}{4} \) (coefficient of \( x \)) and \( b = -12 \) (constant term).

Part J: \( x + 2y = -10 \)

Rewrite in slope-intercept form:

• Step 1: Solve for \( y \):

\( 2y = -x - 10 \)
\( y = -\frac{1}{2}x - 5 \).

• Step 2: Identify \( m \) and \( b \).

Here, \( m = -\frac{1}{2} \) (coefficient of \( x \)) and \( b = -5 \) (constant term).

Part K: \( y = -x - 3 \)

The equation is already in slope-intercept form.

• Step 1: Identify \( m \) and \( b \).

Here, \( m = -1 \) (coefficient of \( x \)) and \( b = -3 \) (constant term).

Part L: \( y = x - 9 \)

The equation is already in slope-intercept form (can be written as \( y = 1x - 9 \)).

• Step 1: Identify \( m \) and \( b \).

Here, \( m = 1 \) (coefficient of \( x \)) and \( b = -9 \) (constant term).

Final Answers (Summarized):

Equation	\( m \)	\( b \)
\( x + y = 8 \)	\( -1 \)	\( 8 \)
\( y = -\frac{1}{2}x - 19 \)	\( -\frac{1}{2} \)	\( -19 \)
\( y - 2 = 3x \)	\( 3 \)	\( 2 \)
\( y = -\frac{1}{5}x + 19 \)	\( -\frac{1}{5} \)	\( 19 \)
\( y = \frac{1}{5}x \)	\( \frac{1}{5} \)	\( 0 \)
\( y + \frac{1}{2}x = 8 \)	\( -\frac{1}{2} \)	\( 8 \)
\( y = x \)	\( 1 \)	\( 0 \)
\( 4y - x = -48 \)	\( \frac{1}{4} \)	\( -12 \)
\( x + 2y = -10 \)	\( -\frac{1}{2} \)	\( -5 \)
\( y = -x - 3 \)	\( -1 \)	\( -3 \)
\( y = x - 9 \)	\( 1 \)	\( -9 \)

(If you need individual answers for each part, use the table or the step-by-step results above.)