Question

multiple choice
for exercises 1–5, choose the correct letter.

1. what is an equation of the line shown in the graph at the right?

a. $y = -\frac{3}{2}x + 4$
c. $y = -\frac{2}{3}x + 4$
b. $y = \frac{2}{3}x + 4$
d. $y = -\frac{2}{3}x + 6$
(graph is a coordinate grid with a line plotted)

1. what is an equation of the line that has slope $-4$ and passes through the point $(-2, -5)$?

f. $y = -4x - 8$
g. $y = -4x - 13$
h. $y = -4x - 5$
i. $y = -4x + 3$

1. what is an equation of the line that passes through the points $(-4, 3)$ and $(-1, 6)$?

a. $y = -x - 7$
b. $y = -x - 1$
c. $y = 7x + 1$
d. $y = x + 7$

1. the data shown in the table is linear. which equation models the data?

f. $y = \frac{1}{2}x + 12$
h. $y = 2x + 9$
g. $y = \frac{1}{2}x + 6$
i. $y = 2x - 3$
(table:

$x$	$y$
6	15
10	17

)

1. karissa earns $200 per week plus $25 per item she sells. which equation models the relationship between her pay $p$ per week and the number of items $n$ she sells?

a. $p = 200n + 25$
c. $n = 25p + 200$
b. $p = 25n + 200$
d. $n = 200p + 25$

short response

1. what is an equation of the line that passes through $(-8, 2)$ and has slope $-\frac{3}{4}$? what is the graph of the equation?

prentice hall algebra 1 • teaching resources
copyright © by pearson education, inc., or its affiliates. all rights reserved.

Explanation:

1. Problem 1: Identify slope-intercept form

Step1: Find y-intercept ($b$)

The line crosses the y-axis at $(0,6)$, so $b=6$.

Step2: Calculate slope ($m$)

Use points $(0,6)$ and $(3,4)$:
$m=\frac{4-6}{3-0}=-\frac{2}{3}$

Step3: Write line equation

$y=mx+b = -\frac{2}{3}x+6$

2. Problem 2: Use point-slope form

Step1: Recall point-slope formula

$y-y_1=m(x-x_1)$ where $m=-4$, $(x_1,y_1)=(-2,-5)$

Step2: Substitute values into formula

$y-(-5)=-4(x-(-2))$

Step3: Simplify to slope-intercept

$y+5=-4(x+2) \implies y+5=-4x-8 \implies y=-4x-13$

3. Problem 3: Calculate slope first

Step1: Compute slope from two points

Points $(-4,3)$ and $(-1,6)$:
$m=\frac{6-3}{-1-(-4)}=\frac{3}{3}=1$

Step2: Substitute to find $b$

Use $(-4,3)$: $3=1(-4)+b \implies b=7$

Step3: Write line equation

$y=1x+7 = x+7$

4. Problem 4: Test slope and intercept

Step1: Calculate slope from table

Use $(2,13)$ and $(6,15)$:
$m=\frac{15-13}{6-2}=\frac{2}{4}=\frac{1}{2}$

Step2: Find y-intercept $b$

Use $(2,13)$: $13=\frac{1}{2}(2)+b \implies 13=1+b \implies b=12$

Step3: Write line equation

$y=\frac{1}{2}x+12$

5. Problem 5: Model linear pay structure

Step1: Identify fixed and variable pay

Fixed pay = $\$200$, variable pay = $\$25$ per item $n$

Step2: Write pay equation

Total pay $p = 25n + 200$

6. Problem 6: Derive line equation

Step1: Use point-slope formula

$m=-\frac{3}{4}$, $(x_1,y_1)=(-8,2)$:
$y-2=-\frac{3}{4}(x-(-8))$

Step2: Simplify to slope-intercept

$y-2=-\frac{3}{4}(x+8) \implies y-2=-\frac{3}{4}x-6 \implies y=-\frac{3}{4}x-4$

Step3: Graph description

The line has a y-intercept at $(0,-4)$ and slope $-\frac{3}{4}$: from any point on the line, move down 3 units and right 4 units (or up 3, left 4) to find another point.

Answer:

1. D. $y = -\frac{2}{3}x + 6$
2. G. $y = -4x - 13$
3. D. $y = x + 7$
4. F. $y = \frac{1}{2}x + 12$
5. B. $p = 25n + 200$
6. Equation: $y=-\frac{3}{4}x-4$; Graph: A line with y-intercept $(0,-4)$ and slope $-\frac{3}{4}$, decreasing from left to right.